CN113111809A - Processing method and system for dynamic synchronous phasor measurement signal of power system - Google Patents

Processing method and system for dynamic synchronous phasor measurement signal of power system Download PDF

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CN113111809A
CN113111809A CN202110423889.4A CN202110423889A CN113111809A CN 113111809 A CN113111809 A CN 113111809A CN 202110423889 A CN202110423889 A CN 202110423889A CN 113111809 A CN113111809 A CN 113111809A
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张和洪
郭文忠
王娟
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Fuzhou University
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Abstract

The invention specifically discloses a method and a system for processing dynamic synchronous phasor measurement signals of a power system, wherein the method comprises the following steps: s1, establishing a general state estimation algorithm according to the synchronous phasor measurement signals given by the power system; s2, constructing a discrete time optimal control algorithm of the overall state estimation algorithm according to the overall state estimation algorithm established in the step S1, and further obtaining a rapid optimal control function. The invention provides a discrete tracking differentiator algorithm based on variable boundary layer thickness, which leads the boundary layer function of the tracking differentiator to be changed according to requirements by introducing damping parameters and rigid parameters representing a power system, improves the phase quality of the algorithm, and has the characteristics of simple structure, less occupied hardware resources and capability of effectively acquiring tracking filtering estimation of a state.

Description

Processing method and system for dynamic synchronous phasor measurement signal of power system
Technical Field
The invention relates to the technical field of power systems, in particular to a method and a system for processing dynamic synchronous phasor measurement signals of a power system.
Background
A Wide Area Measurement System (WAMS) has become a basic component of an automatic scheduling System of a power System, and a Phasor Measurement Unit (PMU) has basically covered most high-voltage substations and key substations. As an important method for monitoring and analyzing the dynamic process of the interconnected power system, the WAMS is continuously expanded in scale, and more advanced application functions are correspondingly developed, such as hybrid state estimation, network parameter identification, load model identification, fault analysis, safety early warning, and the like. The WAMS-based advanced application software functionality is highly dependent on the quality of PMU dynamic data. The synchronous phasor measurement technology provides advanced information technology guarantee for realizing large-area real-time monitoring of a power system, wherein the core foundation of the synchronous phasor measurement technology is the design and implementation of a synchronous phasor estimation algorithm. The estimation accuracy of the algorithm, especially the estimation accuracy in the phase quality aspect, directly affects the effects of other advanced applications of the wide area measurement system, such as hybrid state estimation, network parameter identification, security early warning, and the like. Considering the influence of the environmental noise of the synchronous phasor monitoring device, the inherent noise of the device and the transmission noise, a great amount of random noise is mixed in the real-time measurement signal, and how to effectively obtain the filtering of the dynamic phasor signal and other extension signals is of great importance.
A state estimation algorithm with excellent performance needs to be able to obtain effective filtering and spreading signals (such as differential signals) under the following two conditions: first, when the frequency bandwidth of a given signal changes; second, when random noise interference of different strengths is present for a given signal. Effective filtering and spread signal estimation mainly exhibit two aspects: firstly, the tracking error of the tracking filtering and expanding signal meets the requirement of an actual system; second, the phase lag of the tracking filter with respect to the spread signal is as small as possible in comparison to the given signal. Two more common algorithms mainly exist in signal tracking filtering and signal differentiation perhaps, namely a sliding mode differentiator and a tracking differentiator algorithm based on a sliding mode control algorithm. Levant (1993) provides a sliding mode differentiator which can effectively extract the differentiation of a signal and is applied to sliding mode control, so that a system can realize robust and stable tracking control under the conditions of disturbance and uncertainty. The differentiator is a double sliding mode algorithm and a continuous differential algorithm, but has no corresponding boundary strategy in a discrete form, and has great defects in differential signal extraction in the presence of noise when the frequency band of an input signal changes, slow dynamic process and overshoot phenomenon. Then, Utkin et al deeply researches a Levant differentiator, and applies the sliding mode differentiator to the sliding mode controller design and the sliding mode observer design of a multivariable control system. However, the sliding mode differentiator has a serious problem that the dynamic process is slow and the flutter phenomenon is very prominent, the control quantity requires high-frequency adjustment, and the phase quality is reduced very fast along with the existence of random noise of the signal. Korean Jing Qing scholars in China put forward a thought based on bang-bang control, and a nonlinear tracking differentiator algorithm is introduced. The method has the form of discrete algorithm, and has the advantages of being capable of tracking input signals rapidly without flutter and overshoot and simultaneously extracting effective differential signals. However, when there is a large noise in the processed signal, the tracking filtering of the signal and the estimation of the differential spread signal have a large phase lag problem.
Disclosure of Invention
The invention aims to provide a method and a system for processing dynamic synchronous phasor measurement signals of a power system, which lead the discrete time optimal control for constructing the estimation algorithm to have changeable boundary layer width by introducing two parameters of damping and rigidity, thereby improving the phase quality of the estimation algorithm, and the algorithm has the characteristics of simple structure and less occupied hardware resources.
In order to solve the above technical problem, the present invention provides a method for processing a dynamically synchronized phasor measurement signal in an electrical power system, which comprises the following steps:
s1, establishing an overall state estimation algorithm according to the synchronous phasor measurement signals given by the power system, and expressing the overall state estimation algorithm as follows:
Figure BDA0003029038240000021
in the formula (1), u (k) represents a control quantity of the system, k represents a sampling time of the system, v (k) represents a synchrophasor measurement signal given by the system, h represents a sampling step length of the system, fsp () represents a time optimal control function based on variable system damping, x (k) represents a real-time state of the system,
Figure BDA0003029038240000022
x1and x2Representing the system state on which the time-optimal control function is based during the establishment of the control function, c0Representing a filter factor, r representing a constraint condition of a system control quantity, alpha representing a damping parameter of the system, and beta representing a rigidity parameter of the system;
and S2, constructing a fast optimal control function of the overall state estimation algorithm according to the overall state estimation algorithm established in the step S1.
Preferably, the specific implementation manner of step S2 includes:
s21, introducing a second-order discrete system model with limited control quantity, wherein the second-order discrete system model is expressed as:
x(k+1)＝Ax(k)+Bu(k),|u(k)|≤r (2)
in the formula (2), A and B represent system matrices of a second-order discrete system model,
Figure BDA0003029038240000031
s22, constructing a control sequence which enables any initial state of the system to return to the origin of the system within a limited time, and determining an expression of the initial state of the system according to the second-order discrete system model in the step S21;
s23, the control quantity at the initial time is represented by the expression of the system initial state in the step S22, namely, the fast optimal control function at the initial time can be obtained, and further the fast optimal control function of the overall system state can be obtained.
Preferably, the control sequence in step S22 is formulated as:
Figure BDA0003029038240000032
the expression of the determined system initial state is:
Figure BDA0003029038240000033
in equations (3) and (4), u (i) represents the control amount of the (i +1) th step, i is 0,1,2, …, k represents the number of steps of returning the system initial state to the system origin, x (0) represents the system initial state, a (b) represents the system initial state, and (c) represents the system initial statek+1Representing the expression when the system matrix A is iteratively calculated to k +1, Ak-iRepresenting the expression when the system matrix a is iteratively calculated to k-i.
Preferably, the specific implementation manner of step S23 includes:
s231, firstly, effectively partitioning all points on a phase plane, and simultaneously selecting all values in a control quantity constraint condition to obtain an equal time zone G (k), wherein the equal time zone G (k) is represented as:
Figure BDA0003029038240000034
s232, introducing a nonlinear boundary change function of the system, and then adjusting damping parameters of the characterization system to obtain a boundary curve and a control characteristic curve, wherein the nonlinear boundary change function is expressed as:
y＝βx1+αhx2 (6)；
s233, according to the boundary curve in step S232, the fast optimal control function in the equal time zone G (2) is obtained, that is, the fast optimal control function of the whole state space can be obtained
Preferably, the boundary curve in step S232 includes Γ+And Γ-Wherein
Figure BDA0003029038240000041
And the equation of the curve ΓAExpressed as:
Figure BDA0003029038240000042
equation of the curve ΓBExpressed as:
Figure BDA0003029038240000043
in formula (8), s ═ sign (x)1+hx2) Sign () represents a sign function in mathematics;
control characteristic curve gammaCIs formulated as:
Figure BDA0003029038240000044
preferably, the specific implementation manner of step S233 includes:
s2331, firstly, determining expressions of vertexes of the equal time zones G (1) and G (2), wherein the expression of the vertexes of the equal time zone G (1) is as follows:
Figure BDA0003029038240000045
the expression for the vertices of the equal time zone G (2) is:
Figure BDA0003029038240000046
taking the extreme value r or-r of the control quantity u (i), the vertex of the equal time zone G (1) is expressed as:
Figure BDA0003029038240000047
in the formula (12), a-1And a+1Representing different vertices of the equal time zone G (1);
the isochronal zone G (2) vertex can be expressed as:
Figure BDA0003029038240000051
in the formula (13), a-2、a+2、b-2And b+2Different vertices representing the equal time zone G (2);
s2332, writing a linear equation of the boundary line corresponding to the equal time zones G (1) and G (2) according to the vertexes of the equal time zones G (1) and G (2) acquired in the step S2331, wherein the linear equation of the boundary line corresponding to the equal time zone G (1) is expressed as:
x1＝-hx2 (14)
the equation of the straight line of the boundary line corresponding to the equal time zone G (2) is expressed as:
Figure BDA0003029038240000052
s2333, obtaining a fast optimal control function in the equal time zone G (2) according to a linear equation of the corresponding boundary line of the equal time zones G (1) and G (2) in the step S2332, wherein the initial state of the equal time zone G (2) meets the following conditions:
Figure BDA0003029038240000053
expanding the formula (16) to obtain a system of linear equations:
Figure BDA0003029038240000054
according to formula (17):
Figure BDA0003029038240000055
thereby obtaining a fast optimal control function within the equal time zone G (2), which can be formulated as:
Figure BDA0003029038240000056
s2334, a fast optimal control function of the whole state space can be obtained according to the obtained fast optimal control function in the equal time zone G (2), and the fast optimal control function is expressed as follows by a formula:
Figure BDA0003029038240000061
in the formula (20), d and d0Denotes the intermediate table quantity, d ═ rh, d0＝hd。
A time optimal state estimation system of a power system dynamic synchronization phasor monitoring device comprises a signal receiving module, a processing module, a construction module and a parameter adjusting module, wherein:
the signal receiving module is used for receiving the synchronous phasor measurement signals of the power system and transmitting the received measurement signals;
the processing module is used for determining a boundary curve and a linear change area of the controlled variable based on an introduced second-order discrete system model and a nonlinear boundary change function so as to construct a controlled variable selection rule;
the construction module is used for establishing a total state estimation algorithm according to the measurement signals received by the signal receiving module and then constructing a discrete time optimal control algorithm of the total state estimation algorithm;
the parameter adjusting module is used for acquiring the system state of the power system and effectively acquiring the tracking filtering estimation of the system state through a discrete time optimal control algorithm so as to greatly reduce the tracking filtering and differential extraction phase lag of the measurement signal;
the processing system adopts the processing method of the dynamic synchronous phasor measurement signal of the power system to process signals.
Compared with the prior art, the invention provides a discrete tracking differentiator algorithm based on the variable boundary layer thickness, the boundary layer function of the tracking differentiator can be changed according to requirements by introducing the damping parameter and the rigid parameter representing the power system, so that the phase quality of the algorithm is improved, and the algorithm has the characteristics of simple structure, less occupied hardware resources and effective acquisition of state tracking filtering estimation.
Drawings
FIG. 1 is a flow chart of a method for processing dynamically synchronized phasor measurement signals in a power system according to the present invention,
figure 2 is a flow chart of a method of constructing a discrete time optimal control algorithm of the present invention,
FIG. 3 is a schematic diagram of the equal time zones and the boundary curves in the phase plane of the present invention,
FIG. 4 is a flow chart of a method of obtaining a boundary curve function according to the present invention;
FIG. 5 is a flow chart of a method of determining a fast optimal control synthesis function within the equal time zone G (2) in accordance with the present invention;
FIG. 6 is a diagram showing the estimation effect of the signal tracking filtering state of three common differentiator algorithms in the simulation experiment of the present invention;
FIG. 7 is a diagram showing the estimation effect of the differential signal state of three common differentiator algorithms in the simulation experiment of the present invention;
fig. 8 is a schematic diagram of a processing result of a real-time signal of a selected PMU monitoring device of an electric power system according to an embodiment of the present invention;
fig. 9 is a time optimal state estimation system of a power system dynamic synchronization phasor monitoring apparatus.
In the figure: 11. the device comprises a signal receiving module, 12 a processing module, 13 a construction module and 14 a parameter adjusting module.
Detailed Description
In order to make the technical solutions of the present invention better understood, the present invention is further described in detail below with reference to the accompanying drawings.
As shown in fig. 1 to 2, a method for processing a dynamic synchronous phasor measurement signal of a power system includes the following steps:
s1, establishing an overall state estimation algorithm according to the synchronous phasor measurement signals given by the power system, and expressing the overall state estimation algorithm as follows:
Figure BDA0003029038240000071
in the formula (1), u (k) represents a control quantity of the system, k represents a sampling time of the system, v (k) represents a synchrophasor measurement signal given by the system, h represents a sampling step length of the system, fsp () represents a time optimal control function based on variable system damping, x (k) represents a real-time state of the system,
Figure BDA0003029038240000072
x1and x2Representing the system state on which the time-optimal control function is based during the establishment of the control function, c0Representing a filter factor, r representing a constraint condition of a system control quantity, alpha representing a damping parameter of the system, and beta representing a rigidity parameter of the system;
and S2, constructing a fast optimal control function of the overall state estimation algorithm according to the overall state estimation algorithm established in the step S1.
S21, firstly, introducing a second-order discrete system with limited control quantity, wherein the second-order discrete system is expressed as:
x(k+1)＝Ax(k)+Bu(k),|u(k)|≤r (2)
in the formula (2), A and B represent system matrices of a second-order discrete system,
Figure BDA0003029038240000081
s22, constructing a control sequence which enables any initial state of the system to return to the origin of the system within a limited time, and determining an expression of the initial state of the system according to the second-order discrete system model in the step S21;
s23, the control quantity at the initial time is expressed by the initial state expression of the system in the step S22, namely, the fast optimal control function at the initial time can be obtained, and further the fast optimal control function of the overall state of the system can be obtained.
Wherein the control sequence in step S22 is formulated as:
Figure BDA0003029038240000082
the expression of the determined system initial state is:
Figure BDA0003029038240000083
in equations (3) and (4), u (i) represents the control amount of the (i +1) th step, i is 0,1,2, …, k represents the number of steps of returning the system initial state to the system origin, x (0) represents the system initial state, a (b) represents the system initial state, and (c) represents the system initial statek+1Representing the expression when the system matrix A is iteratively calculated to k +1, Ak-iRepresenting the expression when the system matrix a is iteratively calculated to k-i.
As shown in fig. 4, a specific implementation manner of step S23 includes:
s231, firstly, effectively partitioning all points on a phase plane, and simultaneously selecting all values in a control quantity constraint condition to obtain an equal time zone G (k), wherein the equal time zone G (k) is represented as:
Figure BDA0003029038240000084
s232, introducing a nonlinear boundary change function of the system, and then adjusting damping parameters of the characterization system to obtain a boundary curve and a control characteristic curve, wherein the nonlinear boundary change function is expressed as:
y＝βx1+αhx2 (6)；
s233, according to the boundary curve in the step S232, the fast optimal control function in the equal time zone G (2) is obtained, so that the fast optimal control function of the whole state space can be obtained.
In this embodiment, for the introduced second-order discrete system model and the initial state x (0) given by the system, a control sequence u (0), u (1), …, u (k) is first designed to make any initial state of the system return to the system origin within a limited time. Since the system is a controllable system, for any given initial state, there must be a set of available control sequences u (0), u (1), …, u (k) that enables the initial state to step back to the origin of the system through k +1, i.e. the final state satisfies x (k +1) ═ 0, and when the final state satisfies x (k +1) ═ 0, the expression for the initial state of the system can be deduced back.
Meanwhile, in order to make any state in the phase plane return to the origin of the system under the driving of the corresponding control quantity, all points on the phase plane are effectively partitioned into the boundary layer and the boundary layer, and the control quantity u (i) is taken over all possible values satisfying | u (i) | ≦ r, so as to obtain an expression of the equal time zone G (k), which can be obtained from the graph shown in FIG. 3 and the formula (5), wherein the equal time zone G (k) is a vector [ ih ≦ r2,-h]TI is a linear combination of 0,1, … k, and the weight factor thereof satisfies | u (i) | ≦ r, so that G (k) is a convex 2 k-sided polygon (k is a line segment when 1), and G (1) is a-1,a+1Line segment with vertex G (2) is a-2,a+2,b-2,b+2A parallelogram of vertices. And then introducing a non-linear boundary change function based on the equal time zone G (k), and obtaining different boundary curves and expressions of control characteristic curves by adjusting damping parameters of a representation system and combining u (i) value selection of the control quantity so as to obtain state estimation algorithms with different performances. As can be seen in FIG. 3, one of the boundary curves
Figure BDA0003029038240000091
Is represented by point …, a+k,a+(k-1),…,a+2,b+2,b+3 ,…,b+(k-1),b+k… form, gamma+The lower part is a region where the control quantity u takes + r; another boundary curve
Figure BDA0003029038240000092
Is represented by point …, b-k,b-(k-1),…,b-2,a-2,a-3,…,a-(k-1),a-k… form, gamma-The upper side is a region where the control amount u takes the value of-r. Wherein, point a+kIs the control quantity u is totally taken as + r, along the broken line a+k,a+(k-1),…,a+10, step k back to the initial point of origin, thus connecting point a+k,a+(k-1),…,a+1The broken line of 0 is the fastest trajectory to the origin; likewise, point a-kIs that the controlled quantity u is totally taken as-r, along the broken line a-k,a-(k-1),…,a-10, step k back to the initial point of origin, thus connecting point a-k,a-(k-1),…,a-1The broken line of 0 is the fastest trajectory to the origin; point b-k(b+k) K ≧ 2 is the first-step controlled variable u, taken at-r (+ r), and the state reaches the point a+(k-1)(a-(k-1)) Then, the control quantity u takes + r (-r) and follows the broken line a+(k-1),…,a+1,0(a-(k-1),…,a-10) initial point back to the origin. Line segment [ b-k,a+k]([b+k,a-k]) K is equal to or greater than 2 and line segment [ a ]+1,a-1]Parallel to each other, the middle points c of these line segments+k(c-k) The first step of taking the controlled quantity u is equal to 0, and the state reaches the point a+(k-1)(a-(k-1)) Then, the control quantity u takes + r (-r) and follows the broken line a+(k-1),…,a+1,0(a-(k-1),…,a-10) back to the initial point of the original point, so that a functional expression of the boundary curve and the control characteristic curve, namely a±iAnd i is more than or equal to 2A：
Figure BDA0003029038240000101
b±iAnd i is more than or equal to 2B：
Figure BDA0003029038240000102
(wherein s ═ sign (x)1+hx2) Sign () representing a symbol function in mathematics), and c)±iEquation of the curve where i is greater than or equal to 2C：
Figure BDA0003029038240000103
As shown in fig. 3 and 5, the specific implementation manner of step S233 includes:
s2331, firstly, determining expressions of vertexes of the equal time zones G (1) and G (2), wherein the expression of the vertexes of the equal time zone G (1) is as follows:
Figure BDA0003029038240000104
the expression for the vertices of the equal time zone G (2) is:
Figure BDA0003029038240000105
taking the extreme value r or-r of the control quantity u (i), the vertex of the equal time zone G (1) is expressed as:
Figure BDA0003029038240000106
in the formula (12), a-1And a+1Representing different vertices of the equal time zone G (1);
the isocratic zone G (2) vertices are represented as:
Figure BDA0003029038240000111
in the formula (13), a-2、a+2、b-2And b+2Different vertices representing the equal time zone G (2);
s2332, writing a linear equation of the boundary line corresponding to the equal time zones G (1) and G (2) according to the vertexes of the equal time zones G (1) and G (2) acquired in the step S2331, wherein the linear equation of the boundary line corresponding to the equal time zone G (1) is expressed as:
x1＝-hx2 (14)
the equation of the straight line of the boundary line corresponding to the equal time zone G (2) is expressed as:
Figure BDA0003029038240000112
s2333, obtaining a fast optimal control function in the equal time zone G (2) according to a linear equation of the corresponding boundary line of the equal time zones G (1) and G (2) in the step S2332, wherein the initial state of the equal time zone G (2) meets the following conditions:
Figure BDA0003029038240000113
expanding the formula (16) to obtain a system of linear equations:
Figure BDA0003029038240000114
according to formula (17):
Figure BDA0003029038240000115
thereby obtaining a fast optimal control function within the equal time zone G (2), which can be formulated as:
Figure BDA0003029038240000116
s2335, a fast optimal control function of the whole state space can be obtained according to the obtained fast optimal control function in the equal time zone G (2), and the fast optimal control function is expressed as follows by a formula:
u＝fsp(x1,x2,r,h)
Figure BDA0003029038240000121
in the formula (20), d and d0Denotes the intermediate table quantity, d ═ rh, d0H, wherein h is h, hi,
Figure BDA0003029038240000122
in the present embodiment, the first and second electrodes are,when the initial state of the system is located in the linear region and in the first quadrant and the third quadrant, because there are different choices for the control amount, the situation that two steps can be reached needs to be considered separately, namely, firstly, the expressions of the vertexes of the equal time zones G (1) and G (2) are determined, the extreme value r or-r of the control amount is determined, and then the vertexes of the equal time zones G (1) and G (2) can be obtained, wherein the equal time zone G (1) is formed by the point a1,a-1The line segment formed, and then the line segment [ a ] can be written-1,a+1]In the equation of a straight line, and the equal time zone G (2) is formed by the point a2,b-2,a-2,b2A parallelogram formed by the segments [ a ]-2,b-2]The fast optimal control quantity u ═ r, line segment [ a ═ r+2,b+2]The fast optimum control amount u + r of (1) above because, at the line segment [ c ]-2,c+2]When u is 0, the line segment [ a ] can be reached-1,a+1]I.e., the equal time zone G (1), so that the line segment [ c-2,c+2]The fast optimum control amount u of (1) is 0. Further, a specific equation of the four boundary lines of the equal time zone G (2) can be written, wherein [ a ]-2,b-2]The equation of the straight line is as follows: x is the number of1+2hx2＝y+hx2＝+h2r；[a+2,b+2]The equation of the straight line is as follows: x is the number of1+2hx2＝y+hx2＝-h2r；[a+2,b-2]The equation of the straight line is as follows: y is x1+hx2＝+h2r；[a-2,b+2]The equation of the straight line is as follows: y is x1+hx2＝-h2r; thus, it can be seen that the equal time zone G (2) is a parallelogram surrounded by four line segments, i.e. omega2. Then by waiting for the time zone omega2The control quantity u (0) corresponding to the initial state x (0) of the system can be solved by expanding the condition met by the initial state, so that the expression of the control quantity at the initial time represented by the initial state x (0) of the system can be obtained, the quick optimal control comprehensive function in the equal time zone G (2) can be obtained, the quick optimal control comprehensive function of the whole state space can be obtained, and the quick optimal control comprehensive function of the algorithm function can be seen from the quick optimal control comprehensive function of the whole state spaceThe method has the characteristics of low calculation complexity, no complicated operation process and simple steps.
The invention also provides a time optimal state estimation system of the power system dynamic synchronization phasor monitoring equipment, as shown in fig. 9, comprising a signal receiving module 11, a processing module 12, a construction module 13 and a parameter adjusting module 14, wherein:
the signal receiving module 11 is configured to receive a power system synchronous phasor measurement signal and transmit the received measurement signal;
the processing module 12 is configured to determine a boundary curve and a linear change region of the controlled variable based on an introduced second-order discrete system model and a nonlinear boundary change function, so as to construct a controlled variable selection rule;
a construction module 13, which establishes a total state estimation algorithm according to the measurement signal received by the signal receiving module 11, and then constructs a discrete time optimal control algorithm of the total state estimation algorithm;
the parameter adjusting module 14 is used for acquiring a system state of the power system, and effectively acquiring tracking filtering estimation of the system state through a discrete time optimal control algorithm, so that the tracking filtering and differential extraction phase lag of a measurement signal is greatly reduced;
the processing system adopts the processing method of the dynamic synchronous phasor measurement signal of the power system to process the signal.
Firstly, a signal receiving module 11 receives a measurement signal of a synchronous phasor in a power system, a construction module 13 is utilized to establish a total state estimation algorithm, a discrete time optimal control algorithm is constructed according to the total state estimation algorithm, a processing module 12 is utilized to construct a selection rule of a control quantity, and finally the state of the system is obtained, and tracking filtering of the state of the system is effectively obtained through a parameter adjusting module 14, so that the tracking filtering of the signal and the phase lag of differential extraction are greatly reduced.
In order to better understand the working principle and the technical effect of the invention, three common differentiator algorithms are used for carrying out corresponding simulation experiments.
In the simulation experiment, the first algorithm is a discrete tracking differentiator algorithm based on the thickness of the variable boundary layer, which is recorded as: fsp-TD; the second is an algorithm designed by the scholars in China Han Jing Qing institute, and is written as: fhan-TD; the third is the classical differentiator algorithm commonly used in engineering applications, which is written as: classical D.
Where the input signal is set to v (t) ═ awgn (sin (5t),35), the reference signal is g (t) ═ sin (5t), and a noise signal with a signal-to-noise ratio of 35dB is added to the reference signal using the awgn function. For the fsp-TD parameter chosen as: c. C0＝45；r0300, α is 2, β is 0.25; for the fhan-TD parameter the following are chosen: c. C0＝45；r0300; for the classic D parameter selection: the time constants were 0.01 and 0.02, respectively. The sampling time of the system is set to h-0.001.
As can be seen from fig. 6 and 7, v and dv in fig. 6 and 7 represent theoretical curves, the classical differentiator algorithm has the effect of noise amplification, and when noise exists in the original signal, a smaller time constant results in a larger noise amplification effect. The fhan-TD algorithm can extract smooth filtered and differentiated signals, but the phase quality of the fhan-TD algorithm cannot meet the requirements of practical engineering. The fsp-TD algorithm provided by the invention has the best effect on the aspects of filtering and differential state estimation, and the phase lag is greatly reduced.
As shown in fig. 8, by analyzing and processing real-time data of a PMU monitoring device of a power system, where the real-time data includes node current and voltage magnitude values, a sampling frequency of the real-time data signal is 4960Hz, and corresponding parameters are selected as follows: c. C0＝55；r 0600, 2, 0.25. As can be seen from the figure, the fsp-TD algorithm provided by the invention can effectively filter noise components in real-time signals, the phase lag is small, and the processed result can be directly used in advanced applications such as fault diagnosis and state estimation.
The present invention provides a method and system for processing a dynamic synchronous phasor measurement signal of an electrical power system. The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the core concepts of the present invention. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and such improvements and modifications also fall within the scope of the claims of the present invention.

Claims (7)

1. A processing method for dynamic synchronous phasor measurement signals of a power system is characterized by comprising the following steps:
s1, establishing an overall state estimation algorithm according to the synchronous phasor measurement signals given by the power system, and expressing the overall state estimation algorithm as follows:
Figure FDA0003029038230000011
in the formula (1), u (k) represents a control quantity of the system, k represents a sampling time of the system, v (k) represents a synchrophasor measurement signal given by the power system, h represents a sampling step length of the system, fsp () represents a time optimal control function based on variable system damping and stiffness, and x (k) represents a real-time state of the system,
Figure FDA0003029038230000012
x1and x2Representing the system state on which the time-optimal control function is based during the process of establishing c0Representing a filter factor, r representing a constraint condition of a system control quantity, alpha representing a damping parameter of the system, and beta representing a rigidity parameter of the system;
and S2, constructing a fast optimal control function of the overall state estimation algorithm according to the overall state estimation algorithm established in the step S1.
2. The method for processing the dynamically synchronized phasor measurement signal according to claim 1, wherein the specific implementation manner of step S2 includes:
s21, introducing a second-order discrete system model with limited control quantity, wherein the second-order discrete system model is expressed by a formula as follows:
x(k+1)＝Ax(k)+Bu(k),|u(k)|≤r (2)
in the formula (2), A and B represent system matrices of a second-order discrete system model,
Figure FDA0003029038230000013
s22, constructing a control sequence which enables any initial state of the system to return to the origin of the system within a limited time, and determining an expression of the initial state of the system according to the second-order discrete system model in the step S21;
s23, the control quantity at the initial time is represented by the expression of the system initial state in the step S22, so that the fast optimal control function at the initial time can be obtained, and further the fast optimal control function of the overall system state can be obtained.
3. The method for processing dynamically synchronized phasor measurement signal of electric power system according to claim 2, wherein said control sequence in step S22 can be formulated as:
Figure FDA0003029038230000021
the expression of the determined system initial state is:
Figure FDA0003029038230000022
in equations (3) and (4), u (i) represents the control amount of the (i +1) th step, i is 0,1,2, …, k represents the number of steps of returning the system initial state to the system origin, x (0) represents the system initial state, a (b) represents the system initial state, and (c) represents the system initial statek+1Representing the expression when the system matrix A is iteratively calculated to k +1, Ak-iRepresenting the expression when the system matrix a is iteratively calculated to k-i.
4. The method for processing the dynamically synchronized phasor measurement signal according to claim 3, wherein the specific implementation manner of step S23 includes:
s231, firstly, effectively partitioning all points on a phase plane, and simultaneously selecting all values in a control quantity constraint condition to obtain an equal time zone G (k), wherein the equal time zone G (k) is represented as:
Figure FDA0003029038230000023
s232, introducing a nonlinear boundary change function of the system, and then adjusting damping parameters of the characterization system to obtain a boundary curve and a control characteristic curve, wherein the nonlinear boundary change function is expressed as:
y＝βx1+αhx2 (6)；
s233, according to the boundary curve in the step S232, the fast optimal control function in the equal time zone G (2) is obtained, namely the fast optimal control function of the whole state space can be obtained.
5. The method as claimed in claim 4, wherein the boundary curve of step S232 includes Γ ™+And Γ-Wherein
Figure FDA0003029038230000024
And the equation of the curve ΓAExpressed as:
Figure FDA0003029038230000025
equation of the curve ΓBExpressed as:
Figure FDA0003029038230000031
in formula (8), s ═ sign (x)1+hx2) Sign () represents a sign function in mathematics;
control characteristic curve gammaCIs formulated as:
Figure FDA0003029038230000032
6. the method for processing the dynamically synchronized phasor measurement signal according to claim 5, wherein the specific implementation manner of step S233 includes:
s2331, firstly, determining expressions of vertexes of the equal time zones G (1) and G (2), wherein the expression of the vertex of the equal time zone G (1) is as follows:
Figure FDA0003029038230000033
the expression for the vertices of the equal time zone G (2) is:
Figure FDA0003029038230000034
taking the extreme value r or-r of the control quantity u (i), the vertex of the equal time zone G (1) is expressed as:
Figure FDA0003029038230000035
in the formula (12), a-1And a+1Representing different vertices of the equal time zone G (1);
the isocratic zone G (2) vertices are represented as:
Figure FDA0003029038230000036
in the formula (13), a-2、a+2、b-2And b+2Indicating the difference in the equal time zone G (2)A vertex;
s2332, writing a linear equation of the boundary line corresponding to the equal time zones G (1) and G (2) according to the vertexes of the equal time zones G (1) and G (2) acquired in the step S2331, wherein the linear equation of the boundary line corresponding to the equal time zone G (1) is expressed as:
x1＝-hx2 (14)
the equation of the straight line of the boundary line corresponding to the equal time zone G (2) is expressed as:
Figure FDA0003029038230000041
s2333, obtaining a fast optimal control function in the equal time zone G (2) according to a linear equation of the corresponding boundary line of the equal time zones G (1) and G (2) in the step S2332, wherein the initial state of the equal time zone G (2) meets the following conditions:
Figure FDA0003029038230000042
expanding the formula (16) to obtain a system of linear equations:
Figure FDA0003029038230000043
according to formula (17):
Figure FDA0003029038230000044
thereby obtaining a fast optimal control function within the equal time zone G (2), which is formulated as:
Figure FDA0003029038230000045
s2334, a fast optimal control function of the whole state space can be obtained according to the obtained fast optimal control function in the equal time zone G (2), and the fast optimal control function is expressed as follows by a formula:
Figure FDA0003029038230000046
in the formula (20), d and d0Denotes the intermediate table quantity, d ═ rh, d0＝hd。
7. A processing system for dynamically synchronizing phasor measurement signals of a power system, comprising a signal receiving module (11), a processing module (12), a construction module (13) and a parameter adjustment module (14), wherein:
the signal receiving module (11) is used for receiving and transmitting the synchronous phasor measurement signal of the power system and transmitting the received measurement signal;
the processing module (12) is used for determining a boundary curve and a linear change area of the controlled variable based on an introduced second-order discrete system model and a nonlinear boundary change function so as to construct a controlled variable selection rule;
a construction module (13) which establishes a total state estimation algorithm according to the measurement signal received by the signal receiving module (11) and then constructs a discrete time optimal control algorithm of the total state estimation algorithm;
the parameter adjusting module (14) is used for acquiring the system state of the power system and effectively acquiring the tracking filtering estimation of the system state through a discrete time optimal control algorithm so as to greatly reduce the tracking filtering and differential extraction phase lag of the measurement signal;
the processing system adopts the processing method of the dynamic synchronization phasor measurement signal of the power system as claimed in any one of claims 1 to 6 for signal processing.
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