CN107910880B - Wide-area damping controller optimal parameter setting method based on interval oscillation mode - Google Patents
Wide-area damping controller optimal parameter setting method based on interval oscillation mode Download PDFInfo
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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Abstract
The invention discloses an optimal parameter setting method for a wide-area damping controller based on an interval oscillation mode, which is used for enhancing the damping ratio of a specified interval mode instead of a global mode. These target patterns are reliably tracked during the optimization process by perturbation methods. The optimization model provided by the invention can accurately describe the control characteristics of the WADCs, avoid the occurrence of potential mode shielding conditions and further realize the optimal control performance.
Description
Technical Field
The invention relates to a Wide-Area Damping controller (WADCs) optimal parameter setting method based on an interval oscillation mode.
Background
With the rise of the global energy Internet, the scale of the interconnected power system is gradually increased, and the problem of low-frequency oscillation between the sections is more obvious. The conventional solution is to install a Power System Stabilizer (PSS), but because its feedback control signal is locally sourced, it cannot effectively damp the inter-zone oscillation of the interconnected Power System.
The appearance of a Wide-Area Measurement System (WAMS) brings a new opportunity for the development of stable analysis and control of a large-scale interconnected power System. The interconnected network low-frequency oscillation control based on the wide-area information provided by the WAMS can obtain better damping control performance by introducing the wide-area feedback signal which effectively reflects the interval oscillation mode, provides a new control means for solving the problem of inter-area low-frequency oscillation in the interconnected network and further improving the power transmission capability of the system, and has good and wide application prospect.
Wide-Area Damping Controllers (WADCs) are effective means for solving the problem of low-frequency oscillation between power system intervals. The design of the WADCs includes the selection of the installation location and feedback signals, as well as the tuning of the parameters. One of the main tasks in designing WADCs is to calculate their optimal parameters. Generally, the objective function is to maximize the minimum damping ratio or minimize the real part of the rightmost eigenvalue. However, these optimization problems all suffer from "shadowing," i.e., the optimization process stalls when a mode that is weakly coupled to the WADCs becomes the most critical mode. Obviously, the resulting controller parameters are not optimal since WADCs are essentially uncontrollable and not appreciable for these modes that are weakly coupled thereto.
Disclosure of Invention
The invention aims to solve the problems and provides an optimal parameter setting method for a wide-area damping controller based on an interval oscillation mode, which aims to enhance the damping ratio of a specified interval mode instead of a global mode. The invention focuses on the parameter setting of WADCs, and the installation position and the feedback signal are selected according to a common mode method. These target patterns are reliably tracked during the optimization process by perturbation methods. The optimization model provided by the invention can accurately describe the control characteristics of the WADCs, avoid the occurrence of potential mode shielding conditions and further realize the optimal control performance.
In order to achieve the purpose, the invention adopts the following technical scheme:
the wide area damping controller optimal parameter setting method based on the interval oscillation mode comprises the following steps:
s1: calculating low-frequency oscillation modes of the power system in different operation modes, wherein the oscillation mode smaller than the set damping ratio in each operation mode is a target oscillation mode, and the target oscillation modes in all the operation modes form a target oscillation mode set;
s2: selecting a feedback signal and an installation position of a wide-area damping controller WADCs according to an oscillation mode of a target oscillation mode, and setting initial parameters of the WADCs; establishing a closed-loop time-lag power system model formed by a power system and WADCs corresponding to initial parameters, and calculating a characteristic value of the closed-loop time-lag power system model;
s3: constructing an optimization model taking the minimum damping ratio of the target oscillation mode as a maximum as a target, adding a constraint term in the optimization model to the objective function in a penalty function mode, and rewriting the objective function into a dual mode;
s4: a parameter iteration process, wherein the steepest descent direction and the optimal step length of each parameter iteration are sought;
s5: if the optimal step size module value is smaller than the set error, the optimization is terminated, and the current parameter is the optimal parameter; otherwise, obtaining a new parameter according to the steepest descent direction and the optimal step length; establishing a closed-loop time-lag power system model formed by a power system and WADCs corresponding to new parameters, and calculating a characteristic value of the closed-loop time-lag power system model;
s6: matching the target oscillation mode based on the characteristic value obtained in the step S5, and constructing an optimization model taking the minimum damping ratio of the target oscillation mode as a maximum as a target; adding a constraint term in the optimization model to the objective function in a penalty function mode, and rewriting the objective function into a dual mode;
s7: if the module value of the difference between the function value obtained in the S6 and the function value obtained in the S3 is smaller than the set error, the optimization is terminated, and the current parameter is the optimal parameter of the wide-area damping controller; otherwise, go to S4.
BFGS，Broyden-Fletcher-Goldfarb-Shanno。
In step S1, the different operation modes include: and the normal operation mode is an operation mode in which a line is broken and an operation mode in which a power system has a tidal current change.
In step S1, the target mode is selected while considering different operation modes. In practical power systems, there are different degrees of coupling between multiple low frequency oscillation modes, and each WADCs is used to damp one or more inter-coupled interval low frequency oscillations.
The oscillation mode refers to a right eigenvector, and comprises: amplitude and angle;
setting the initial iteration number l as 1, and setting the initial parameter p of the WADCs(l)。
In the step S2, the power system, the WADCs, the feedback time lag, and the output time lag form a closed-loop time lag power system model in consideration of the delay of tens to hundreds of milliseconds existing in the transmission and processing process of the wide-area signal.
Closed-loop time-lag power system model: when the signals of the power system are output to WADCs, output time lag exists, and the signals output to the WADCs by the power system are selected as a relative power angle, a relative angular speed and an active power difference of two connecting lines between two generators; when the signal of WADCs is input to the power system, a feedback time lag exists, and the signal of WADCs is input to the power system and serves as an input signal of the excitation regulator of the generator.
A closed-loop time-lag power system model represented as:
wherein the content of the first and second substances,is a system state matrix and is a dense matrix. n is the total number of the system state variables;
the state matrix is a system time-lag state matrix and is a sparse matrix;
0<τ1<…<τmis the time lag constant of a time lag link, wherein the maximum time lag is taum；
And lambda is a characteristic value, and v is a right eigenvector corresponding to the characteristic value lambda.
The characteristic value of a closed-loop time-lag power system model is calculated by adopting a large-scale time-lag power system characteristic value calculation method based on EIGD (EIGD) < 201510055743.3 > P </SUB > in Chinese invention patents [1] bulgas, Wang swallow, Liuyutian >.
In step S1, the oscillation modes other than the target oscillation mode in all the operation modes form another oscillation mode set.
In step S1, it is assumed that n is consideredpAn operation mode, wherein the oscillation mode smaller than the set damping ratio is designated as a target oscillation mode in the jth operation mode to form a target oscillation mode set in the jth operation mode
Order toRepresents npThe target oscillation mode set in one operation mode has
Order toIndicating oscillations outside the target oscillation mode in the jth operating modeA collection of patterns.
Order to
Wherein the content of the first and second substances,represents npA set of oscillation modes other than the target oscillation mode in the respective operation modes;
representing the set of all oscillation modes.
In the step S3, the initial parameter p is analyzed(l)And selecting a target oscillation mode corresponding to the power system according to the oscillation mode of the electromechanical oscillation mode of the closed-loop time-delay power system formed by the corresponding WADCs, wherein l is the iteration number.
The optimization model in the step S3 and the step S6 includes an objective function and a constraint condition.
An objective function:
constraint conditions are as follows:
wherein max represents the maximum value and min represents the minimum value;
ζIrepresenting the minimum damping ratio of the target oscillation mode under different operation modes;
ζ (λ) represents a damping ratio of the characteristic value λ; re (λ) represents the real part of the eigenvalue λ; α represents the maximum limit of the real part of the target mode, a typical value of α is taken to be 0.05.
Indicates the j operation modeThe minimum damping ratio of the medium mode,
indicates the j operation modeThe maximum real part of the medium mode;
Ks,krepresents the gain of the kth WADCs;representing the upper limit of the magnification, a typical value is taken to be 100,the lower limit of the magnification is indicated, and a typical value is taken to be 0.1.
T1,k～T4,kTime constants representing lead-lag elements for the kth WADCs;
represents the time constant T1,k～T4,kTypical value of (2) is 5.0;
represents the time constant T1,k～T4,kThe typical value of (1) is 0.02;
ncindicates the number of WADCs.
p is 5n to be setcA parameter comprising: wide area damping controller gain Ks,kAnd time constant T1,k～T4,k。
The formula (1.2) represents that the optimization function of parameter setting aims at maximizing the minimum damping ratio of the target oscillation mode;
the real parts of all characteristic values of the closed-loop time-lag power system model are required to be smaller than-alpha in the formula (1.3), so that the robustness of the wide-area damping controller is improved;
the equations (1.4) and (1.5) ensure that the small disturbance stability of the power system is not weakened by the parameter setting of the WADCs;
equations (1.6) and (1.7) are limit constraints on the wide-area damping controller parameters.
The optimization model in the step S3 and the step S6 is a non-smooth, non-linear, non-convex constraint optimization problem, and is solved by a mathematical programming method. Firstly, the constraint condition is rewritten into a penalty function item of the objective function, and then the penalty function item is rewritten into a dual form, so that an optimization problem is obtained:
in the formula, k1、kj+1、And ωkIs a penalty factor.
The step S4: and calculating a descending direction at the differentiable point of the target function pair parameter by adopting BFGS, calculating the descending direction at the non-differentiable point by adopting a gradient sampling technology, and searching an optimal step length according to a weak Wolfe criterion.
In the step S4, the steepest descent direction in the ith iteration is assumedIs denoted by d(l)And calculating the descending direction by adopting BFGS at the differentiable point of the target function to the parameter:
wherein the content of the first and second substances,representing the gradient vector of the objective function J at the i-th iteration.
H(l)The hessian matrix representing the ith iteration, i.e., the second derivative of the objective function with respect to the parameters.
Assuming that the first and second iterations are the first iteration and the (l + 1) th iteration, the parameter variation value s(l)And gradient vector change value y(l)Are respectively defined as:
wherein p is(l+1)The parameter value representing the (l + 1) th iteration,represents the gradient vector of the objective function J at the l +1 th iteration.
Hessian matrix H for the l +1 th iteration(l+1)：
In which I is the number of dimensions 5ncThe identity matrix of (2). T denotes a matrix transposition.
And (3) calculating the descending direction by adopting a gradient sampling technology at the non-differentiable point of the objective function to the parameters:
first, if the objective function is to the parameter p in the first iteration(l)Irreducible, Clarke's sub-differential defining this point asClarke's sub-differential is a set of points near the non-differentiable point by the objective functionA convex hull of gradient composition of (a);
wherein, conv represents a convex hull,representing the gradient of the objective function at the parameter point p,the expression parameter point p approaches p(l)The limit of the time objective function to the gradient of the parameter point. At point p not differentiable(l)The center of the circle is the sampling part point composition in the sphere with epsilon as the radius
Then, the non-smooth steepest descent direction d of the non-differentiable point(l)Is defined asAnd the reverse direction of the vector with the minimum intermediate norm is obtained by quadratic programming according to the gradient value of the target function of the sampling point:
in the formula, arg represents an angle, min represents a minimum value, and | z | | | represents a norm of z.
In the step S4, it is assumed that the steepest descent direction d is obtained in the calculation in the ith iteration(l)Then, the step t of the following Wolfe search will be satisfied(l)As the optimal step size.
Wherein the factor satisfies 0. ltoreq. alpha1<α2<1，α10 and α2＝0.5。P is expressed at a parameter point(l)+t(l)d(l)And (4) gradient.
In step S5, if the optimum step size modulus | t(l)| is less than the set ε1Then the optimization is terminated, with the current parameter p(l)The optimal parameter is obtained; otherwise, according to the steepest descent direction d(l)And an optimal step size t(l)Obtaining a new parameter set p(l+1)＝p(l)+t(l)d(l)。
The tracking of the target pattern based on the perturbation theory in the step S6 is consistent with the matching method of the power system oscillation pattern in [2] buehua, liuyutian, songsu ] and [ 201410027613.4 ] the matching method of the power system oscillation pattern based on the matrix perturbation theory.
In the step S7, if the function value J (p)(l+1)) And function value J (p)(l)) The modulus of the difference is less than the set error epsilon2Then the optimization is terminated, with the current parameter p(l+1)The optimal parameter is obtained; otherwise, let iteration number l ← l +1 go to S4.
The invention has the beneficial effects that:
firstly, the method for setting the optimal parameters of the wide-area damping controller based on the interval oscillation mode tracking is used for fully considering the influence of time lag when the actual wide-area damping controller is designed.
Secondly, the method for setting the optimal parameters of the wide-area damping controller based on the interval oscillation mode tracking, provided by the invention, has the core innovation point that the performance of the damping controller can be fully exerted aiming at improving the damping ratio of a target mode, and the possible shielding phenomenon is avoided.
Thirdly, the method for setting the optimal parameters of the wide-area damping controller based on the interval oscillation mode tracking, provided by the invention, adopts the perturbation method to ensure that the target mode can be reliably and effectively tracked in the two iterative processes.
Fourthly, the method for setting the optimal parameters of the wide area damping controller based on the interval oscillation mode tracking adopts a numerical algorithm to solve, combines the BFGS and the gradient sampling technology during gradient solving, and avoids the situation of falling into suboptimal solution.
Fifthly, the method for setting the optimal parameters of the wide-area damping controller based on the interval oscillation mode tracking, which is provided by the invention, can also be used for designing the damping controller in the area, the time lag influence is not required to be considered, and the characteristic value of the system is calculated by adopting a conventional characteristic value calculation method.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of a 16-machine 68 node.
FIGS. 3(a) and 3(b) illustrate the optimization process of the proposed method of the present inventionAndthe variation curve of the minimum damping ratio of the medium mode.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. 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 application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1: the optimal parameter setting method of the WADCs based on the interval oscillation mode tracking comprises the following steps:
s1: calculating low-frequency oscillation modes of the power system in different operation modes, wherein the oscillation mode smaller than the set damping ratio in each operation mode is a target oscillation mode, and the target oscillation modes in all the operation modes form a target oscillation mode set;
s2: selecting a feedback signal and an installation position of a wide-area damping controller WADCs according to an oscillation mode of a target oscillation mode, and setting initial parameters of the WADCs; establishing a closed-loop time-lag power system model formed by a power system and WADCs corresponding to initial parameters, and calculating a characteristic value of the closed-loop time-lag power system model;
s3: constructing an optimization model taking the minimum damping ratio of the target oscillation mode as a maximum as a target, adding a constraint term in the optimization model to the objective function in a penalty function mode, and rewriting the objective function into a dual mode;
s4: a parameter iteration process, wherein the steepest descent direction and the optimal step length of each parameter iteration are sought; the steepest descent direction is calculated according to the BFGS method (Broyden-Fletcher-golden farb-Shanno, BFGS) and gradient sampling techniques, and the optimal step size is searched according to the weak Wolfe criterion. And calculating the descending direction of the differentiable point of the target function pair parameter by adopting BFGS, and calculating the descending direction of the differentiable point by adopting a gradient sampling technology.
S5: if the optimal step size module value is smaller than the set error, the optimization is terminated, and the current parameter is the optimal parameter; otherwise, obtaining a new parameter according to the steepest descent direction and the optimal step length; establishing a closed-loop time-lag power system model formed by a power system and WADCs corresponding to new parameters, and calculating a characteristic value of the closed-loop time-lag power system model;
s6: matching the target oscillation mode based on the characteristic value obtained in the step S5, and constructing an optimization model taking the minimum damping ratio of the target oscillation mode as a maximum as a target; adding a constraint term in the optimization model to the objective function in a penalty function mode, and rewriting the objective function into a dual mode;
s7: if the module value of the difference between the function value obtained in the S6 and the function value obtained in the S3 is smaller than the set error, the optimization is terminated, and the current parameter is the optimal parameter of the wide-area damping controller; otherwise, go to S4.
To this end, the optimal parameters of the wide area damping controller have been calculated.
In step S1, the selection of the target mode needs to consider a plurality of operation modes at the same time. In practical power systems, there may be varying degrees of coupling between multiple low frequency oscillation modes, and each WADC may be used to damp one or more inter-coupled interval low frequency oscillations. Suppose n is consideredpAn operation mode, wherein the oscillation mode smaller than the set damping ratio is designated as a target oscillation mode in the jth operation mode to form a target oscillation mode set in the jth operation mode
Order toRepresents npThe target oscillation mode set in one operation mode has
Order toAnd represents a set of oscillation modes other than the target oscillation mode in the j-th operation mode.
Order to
Wherein the content of the first and second substances,represents npA set of oscillation modes other than the target oscillation mode in the respective operation modes;
representing the set of all oscillation modes.
In the step S2, considering that there is a delay of several tens to several hundreds of milliseconds in the transmission and processing of the wide area signal, the power system and the WADCs, and the feedback time lag and the output time lag form a closed-loop time lag power system model. The linearized closed-loop time-lag power system characteristic equation can be expressed as:
in the formula:is a system state matrix and is a dense matrix. And n is the total number of the system state variables.Is a system time-lag state matrix and is a sparse matrix. 0<τ1<…<τmIs the time lag constant of a time lag link, wherein the maximum time lag is taum. λ is a certain eigenvalue, and v is a right eigenvector corresponding to the eigenvalue λ.
And calculating the characteristic value of the time-lag system by adopting a method based on spectrum discretization.
In the step S3, the initial parameter p is analyzed(l)And selecting a target oscillation mode corresponding to the power system according to the oscillation mode of the electromechanical oscillation mode of the closed-loop time-delay power system formed by the corresponding WADCs, wherein l is the iteration number.
The optimization model of parameter tuning in the step S3 and the step S6 includes an objective function and a constraint condition.
The objective function is:
constraint conditions are as follows:
wherein max represents the maximum value and min represents the minimum value;
ζIrepresenting the minimum damping ratio of the target oscillation mode under different operation modes;
ζ (λ) represents a damping ratio of the characteristic value λ; re (λ) represents the real part of the eigenvalue λ; α represents the maximum limit of the real part of the target mode, a typical value of α is taken to be 0.05.
Indicates the j operation modeThe minimum damping ratio of the medium mode,
indicates the j operation modeThe maximum real part of the medium mode;
Ks,krepresents the gain of the kth WADCs;representing the upper limit of the magnification, a typical value is taken to be 100,the lower limit of the magnification is indicated, and a typical value is taken to be 0.1.
T1,k～T4,kTime constants representing lead-lag elements for the kth WADCs;
represents the time constant T1,k～T4,kTypical value of (2) is 5.0;
represents the time constant T1,k～T4,kThe typical value of (1) is 0.02;
ncindicates the number of WADCs.
p is 5n to be setcA parameter comprising: wide area damping controller gain Ks,kAnd time constant T1,k～T4,k。
The formula (1.2) represents that the optimization function of parameter setting aims at maximizing the minimum damping ratio of the target oscillation mode;
the real parts of all characteristic values of the closed-loop time-lag power system model are required to be smaller than-alpha in the formula (1.3), so that the robustness of the wide-area damping controller is improved;
the equations (1.4) and (1.5) ensure that the small disturbance stability of the power system is not weakened by the parameter setting of the WADCs;
equations (1.6) and (1.7) are limit constraints on the wide-area damping controller parameters.
The optimization model in the step S3 and the step S6 is a non-smooth, non-linear, non-convex constraint optimization problem, and is solved by a mathematical programming method. Firstly, the constraint condition is rewritten into a penalty function item of the objective function, and then the penalty function item is rewritten into a dual form, so that an optimization problem is obtained:
in the formula, k1、kj+1、And ωkIs a penalty factor.
In step S4, it is assumed that the steepest descent direction in the ith iteration is denoted by d(l)And the solution adopts a method combining BFGS method and gradient sampling technology calculation.
And calculating the descending direction by adopting BFGS at the differentiable point of the target function to the parameter:
in the formula (I), the compound is shown in the specification,representing the gradient vector of the objective function J at the i-th iteration.
H(l)The hessian matrix representing the ith iteration, i.e., the second derivative of the objective function with respect to the parameters.
Assume two iterations, i.e. the first and l +1 times, before and after the parameter change value s(l)And gradient vector change value y(l)Are respectively defined as:
in the formula, p(l+1)The parameter value representing the (l + 1) th iteration,represents the gradient vector of the objective function J at the l +1 th iteration.
Hessian matrix H for the l +1 th iteration(l+1)Can be calculated from the following formula
In which I is the number of dimensions 5ncThe identity matrix of (2). T denotes a matrix transposition.
And (3) calculating the descending direction by adopting a gradient sampling technology at the non-differentiable point of the objective function to the parameters:
first, if the objective function is to the parameter p in the first iteration(l)Irreducible, Clarke's sub-differential defining this point asClarke's sub-differential is a set of points near the non-differentiable point by the objective functionThe convex hull of the gradient composition of (1) can be expressed specifically as
In the formula, conv represents a convex hull,representing the gradient of the objective function at the parameter point p,the expression parameter point p approaches p(l)The limit of the time objective function to the gradient of the parameter point. At point p not differentiable(l)The sampling part point in the sphere which is used as the center of circle and takes a smaller number epsilon as the radius
Then, the non-smooth steepest descent direction d of the non-differentiable point(l)Can be defined asThe opposite direction of the vector with the minimum medium norm can be obtained by quadratic programming according to the gradient value of the target function of the sampling point.
In the formula, arg represents an angle. min represents the minimum value, | z | | represents the norm of z.
In the step S4, it is assumed that the steepest descent direction d is obtained in the calculation in the ith iteration(l)Then, the step t of the following Wolfe search will be satisfied(l)As the optimal step size.
Wherein the factor satisfies 0. ltoreq. alpha1<α2<1, which is generally taken as alpha in practical calculations10 and α2＝0.5。P is expressed at a parameter point(l)+t(l)d(l)And (4) gradient.
In step S5, if the optimum step size modulus | t(l)| is less than the set ε1Then the optimization is terminated, with the current parameter p(l)The optimal parameter is obtained; otherwise, according to the steepest descent direction d(l)And an optimal step size t(l)Obtaining a new parameter set p(l+1)＝p(l)+t(l)d(l)。
The tracking of the target pattern based on the perturbation theory in the step S6 is consistent with the matching method of the power system oscillation pattern in [2] buehua, liuyutian, songsu ] and [ 201410027613.4 ] the matching method of the power system oscillation pattern based on the matrix perturbation theory.
In the step S7, if the function value J (p)(l+1)) And function value J (p)(l)) The modulus of the difference is less than the set error epsilon2Then the optimization is terminated, with the current parameter p(l+1)The optimal parameter is obtained; otherwise, let iteration number l ← l +1 go to S4.
And verifying the effectiveness of the wide-area damping controller optimal parameter setting method based on interval oscillation mode tracking, which is provided by the invention, by utilizing a 16-machine 68 node arithmetic system. All analyses were performed in Matlab and on an Inter 3.4GHz 8GBRAM desktop computer.
A 16 machine 68 node system is shown in figure 2. The 16-machine 68 node System is an equivalent System connected to the New England Test System (NETS) and New York Power System (NYPS). It comprises 16 generators and 68 nodes, and is divided into 5 areas. Among them, the generators G1-G9 represent New England Test Systems (NETS), the generators G10-G13 represent New York power systems (ny), and the remaining three generators G14-G16 represent equivalent machines connected to three adjacent power systems of ny.
The present invention considers 3 operation modes, and in the reference operation mode #1, there are two weak damping zone low-frequency oscillation modes as target modes. The frequency and damping ratio of mode 1 are 0.43Hz and 0.08%, respectively, which are the interval oscillation modes of G14-G16 relative to G1-G13. By mounting WADC on G5 to improve damping of mode 1, the feedback signals are relative rotor angular velocities Δ ω of G13 and G113-1Feedback time lag of τf1150ms, output time lag τo1100 ms. The frequency and damping ratio of mode 2 are 0.65Hz and 1.21%, respectively, which are the interval oscillation modes of G1-G9 relative to G10-G13. By mounting WADC on G6 to improve damping of mode 2, the feedback signals are relative rotor angular velocities Δ ω of G15 and G615-6Feedback time lag of τf1120ms, output time lag τo1＝90ms。
By the optimal parameter setting method, the optimal parameters of two WADCs can be obtainedAre each Ks1＝56.97，T1,1＝0.20s，T1,2＝0.05s，T1,3＝0.20s，T1,4＝0.05s；Ks2＝55.82，T2,1＝0.20s，T2,2＝0.05s，T2,3＝0.21s，T2,40.05 s. The CPU calculation time was 509 s.
To verify the effectiveness of the optimization model proposed by the present invention, and compared with the model aiming at maximizing the minimum damping ratio of the system, fig. 3(a) and 3(b) show the optimization process of the two models in the operation mode #1Andthe variation curve of the minimum damping ratio of the medium mode. Wherein the content of the first and second substances,the minimum damping ratio of the middle mode is expressed as ζRI.e. byAs can be seen from fig. 3(a) and 3(b), in the first 6 iterations of both methods,damping of mid-range oscillation modes less thanDamping of medium mode. From iteration 7, the minimum damping mode occursIn (1). If a model is used that targets the system minimum damping ratio maximization,interval mode in (1) is completelyThe mode masking in (1). As can be seen from FIGS. 3(a) and 3(b), when the optimization is terminated, ζIFrom 0.43% to 3.28%. On the contrary, the method provided by the invention is adopted to reliably track in each iterationThe target mode in (1) can completely avoid the shielding phenomenon. Optimized zetaIReaching 7.16%. Optimized ζ under operating modes #2 and #3I7.16% and 12.55% respectively can be achieved. According to the data, the damping of the target mode can be obviously improved by installing the optimal controller obtained by the method, and the effectiveness of the wide-area damping controller optimal parameter setting method based on the interval oscillation mode tracking provided by the invention is verified.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (10)
1. The wide area damping controller optimal parameter setting method based on the interval oscillation mode is characterized by comprising the following steps of:
s1: calculating low-frequency oscillation modes of the power system in different operation modes, wherein the oscillation mode smaller than the set damping ratio in each operation mode is a target oscillation mode, and the target oscillation modes in all the operation modes form a target oscillation mode set;
s2: selecting a feedback signal and an installation position of a wide-area damping controller WADCs according to an oscillation mode of a target oscillation mode, and setting initial parameters of the WADCs; establishing a closed-loop time-lag power system model formed by a power system and WADCs corresponding to initial parameters, and calculating a characteristic value of the closed-loop time-lag power system model;
s3: constructing an optimization model taking the minimum damping ratio of the target oscillation mode as a maximum as a target, adding a constraint term in the optimization model to the objective function in a penalty function mode, and rewriting the objective function into a dual mode;
s4: a parameter iteration process, wherein the steepest descent direction and the optimal step length of each parameter iteration are sought;
s5: if the optimal step size module value is smaller than the set error, the optimization is terminated, and the current parameter is the optimal parameter; otherwise, obtaining a new parameter according to the steepest descent direction and the optimal step length; establishing a closed-loop time-lag power system model formed by a power system and WADCs corresponding to new parameters, and calculating a characteristic value of the closed-loop time-lag power system model;
s6: matching the target oscillation mode based on the characteristic value obtained in the step S5, and constructing an optimization model taking the minimum damping ratio of the target oscillation mode as a maximum as a target; adding a constraint term in the optimization model to the objective function in a penalty function mode, and rewriting the objective function into a dual mode;
s7: if the module value of the difference between the function value obtained in the S6 and the function value obtained in the S3 is smaller than the set error, the optimization is terminated, and the current parameter is the optimal parameter of the wide-area damping controller; otherwise, go to S4.
2. The wide-area damping controller optimal parameter setting method based on interval oscillation mode as claimed in claim 1,
in step S1, the different operation modes include: a normal operation mode, an operation mode that a line is broken and an operation mode that a power system has a trend change;
the oscillation mode refers to a right eigenvector, and comprises: amplitude and angle;
setting the initial iteration number l as 1, and setting the initial parameter p of the WADCs(l)。
3. The wide-area damping controller optimal parameter setting method based on interval oscillation mode as claimed in claim 1, characterized in that the closed-loop time-lag power system model: when the signals of the power system are output to WADCs, output time lag exists, and the signals output to the WADCs by the power system are selected as a relative power angle, a relative angular speed and an active power difference of two connecting lines between two generators; when the signal of WADCs is input to the power system, a feedback time lag exists, and the signal of WADCs is input to the power system and serves as an input signal of the excitation regulator of the generator.
4. The wide-area damping controller optimal parameter setting method based on interval oscillation mode as claimed in claim 1, characterized in that the closed-loop time-lag power system model is expressed as:
wherein the content of the first and second substances,is a system state matrix and is a dense matrix; n is the total number of the system state variables;
is a matrix of system time-lag states,is a sparse matrix;
0<τ1<…<τmis the time lag constant of a time lag link, wherein the maximum time lag is taum；
And lambda is a characteristic value, and v is a right eigenvector corresponding to the characteristic value lambda.
5. The method for tuning optimal parameters of a wide-area damping controller based on interval oscillation modes as claimed in claim 1, wherein in step S1, other oscillation modes except the target oscillation mode in all operation modes are formed into other oscillation mode sets;
in step S1, it is assumed that n is consideredpAn operation mode in which an oscillation mode smaller than a set damping ratio is designated as a target oscillation modeForm a target oscillation mode set in the jth operation modej＝1，…，np；
Order toRepresents npThe target oscillation mode set in one operation mode has
Order toA set of oscillation modes other than the target oscillation mode in the jth operation mode;
order to
Wherein the content of the first and second substances,represents npA set of oscillation modes other than the target oscillation mode in the respective operation modes;
representing the set of all oscillation modes.
6. The wide-area damping controller optimal parameter setting method based on interval oscillation mode as claimed in claim 5, wherein the optimization model in the step S3 and the step S6 comprises an objective function and a constraint condition;
an objective function:
constraint conditions are as follows:
wherein max represents the maximum value and min represents the minimum value;
ζIrepresenting the minimum damping ratio of the target oscillation mode under different operation modes;
ζ (λ) represents a damping ratio of the characteristic value λ; re (λ) represents the real part of the eigenvalue λ; - α represents the maximum limit of the real part of the target mode;
indicates the j operation modeThe minimum damping ratio of the medium mode,
indicates the j operation modeThe maximum real part of the medium mode;
Ks,krepresents the gain of the kth WADCs;represents the upper limit of the magnification, takes the value of 100,represents the lower limit of the magnification;
T1,k～T4,ktime constants representing lead-lag elements for the kth WADCs;
represents the time constant T1,k～T4,kAn upper limit value of (d);
represents the time constant T1,k～T4,kA lower limit value of (d);
ncindicates the number of WADCs;
p is 5n to be setcA parameter comprising: wide area damping controller gain Ks,kAnd time constant T1,k～T4,k；
The formula (1.2) represents that the optimization function of parameter setting aims at maximizing the minimum damping ratio of the target oscillation mode;
the real parts of all characteristic values of the closed-loop time-lag power system model are required to be smaller than-alpha in the formula (1.3), so that the robustness of the wide-area damping controller is improved;
the equations (1.4) and (1.5) ensure that the small disturbance stability of the power system is not weakened by the parameter setting of the WADCs;
equations (1.6) and (1.7) are limit constraints on wide-area damping controller parameters;
the optimization model in the step S3 and the step S6 is a non-smooth, non-linear and non-convex constraint optimization problem, and is solved by a mathematical programming method;
firstly, the constraint condition is rewritten into a penalty function item of the objective function, and then the penalty function item is rewritten into a dual form, so that an optimization problem is obtained:
in the formula, k1、kj+1、And ωkIs a penalty factor.
7. The wide-area damping controller optimal parameter setting method based on interval oscillation mode as claimed in claim 1, wherein said step S4: and calculating a descending direction at the differentiable point of the target function pair parameter by adopting BFGS, calculating the descending direction at the non-differentiable point by adopting a gradient sampling technology, and searching an optimal step length according to a weak Wolfe criterion.
8. The wide-area damping controller optimal parameter setting method based on interval oscillation mode as claimed in claim 7, wherein in the step S4, it is assumed that in the I iteration, the steepest descent direction is represented as d(l)And calculating the descending direction by adopting BFGS at the differentiable point of the target function to the parameter:
wherein the content of the first and second substances,gradient vectors representing the objective function J at the l-th iteration;
H(l)hessian matrix representing the l iteration, i.e. the objectThe second derivative of the function with respect to the parameter;
assuming that the first and second iterations are the first iteration and the (l + 1) th iteration, the parameter variation value s(l)And gradient vector change value y(l)Are respectively defined as:
wherein p is(l+1)The parameter value representing the (l + 1) th iteration,gradient vectors representing the l +1 th iteration of the objective function J;
hessian matrix H for the l +1 th iteration(l+1)：
In which I is the number of dimensions 5ncThe identity matrix of (1); t represents matrix transposition;
and (3) calculating the descending direction by adopting a gradient sampling technology at the non-differentiable point of the objective function to the parameters:
first, if the objective function is to the parameter p in the first iteration(l)Irreducible, Clarke's sub-differential defining this point asClarke's sub-differential is a set of points near the non-differentiable point by the objective functionA convex hull of gradient composition of (a);
wherein, conv represents a convex hull,representing the gradient of the objective function at the parameter point p,the expression parameter point p approaches p(l)The extreme value of the time objective function to the gradient of the parameter point; at point p not differentiable(l)The center of the circle is the sampling part point composition in the sphere with epsilon as the radius
Then, the non-smooth steepest descent direction d of the non-differentiable point(l)Is defined asAnd the reverse direction of the vector with the minimum intermediate norm is obtained by quadratic programming according to the gradient value of the target function of the sampling point:
in the formula, arg represents an angle, min represents a minimum value, and | z | | | represents a norm of z;
in the step S4, it is assumed that the steepest descent direction d is obtained in the calculation in the ith iteration(l)Then, the step t of the following Wolfe search will be satisfied(l)As the optimal step length:
wherein the factor satisfies 0. ltoreq. alpha1<α2<1，α10 and α2＝0.5；P is expressed at a parameter point(l)+t(l)d(l)And (4) gradient.
9. The zone-based according to claim 1The optimal parameter setting method of the wide area damping controller in the inter-oscillation mode is characterized in that in the step S5, if the optimal step size module value | t(l)| is less than the set ε1Then the optimization is terminated, with the current parameter p(l)The optimal parameter is obtained; otherwise, according to the steepest descent direction d(l)And an optimal step size t(l)Obtaining a new parameter set p(l+1)＝p(l)+t(l)d(l)。
10. The wide-area damping controller optimal parameter setting method based on interval oscillation mode as claimed in claim 1, wherein in said step S7, if the function value J (p) is(l+1)) And function value J (p)(l)) The modulus of the difference is less than the set error epsilon2Then the optimization is terminated, with the current parameter p(l+1)The optimal parameter is obtained; otherwise, let iteration number l ← l +1 go to S4.
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