CN111864730B - Tracking and identifying method for equivalent parameters of power grid - Google Patents
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Abstract
The invention discloses a tracking and identifying method for equivalent parameters of a power grid, which comprises the following steps of: s1: extracting a voltage and current signal at a first moment after disturbance and a voltage and current signal at a second moment after disturbance from a port of the power network to be equalized, calculating voltage and current transient state electric quantity data, establishing a voltage and current high-order differential equation at two sides of the port of the power network to be equalized and a voltage and current high-order differential equation of the whole power network to be equalized, and solving coefficients of the high-order differential equations; s2: and obtaining and simplifying the high-order differential equations of the voltage and current steady-state electric quantity at two sides of the port of the power network to be equivalent from each established high-order differential equation, enabling the high-order differential equations to be consistent with the forms of the power network equivalent simple network differential equations at two sides of the port, calculating power network equivalent simple network parameters according to the coefficients of the high-order differential equations, and realizing the tracking identification of the power network equivalent parameters. The method realizes tracking identification of equivalent parameters of the power grid by using the voltage, current and electric quantity in the running state of the power grid, can track the parameter characteristics of the running state of the power grid, and can provide an analysis basis for static stability and dynamic stability judgment of the power grid.
Description
Technical Field
The invention relates to the field of power grid analysis and operation, in particular to a power grid equivalent parameter tracking identification method.
Background
Real-time tracking and online analysis of the operation state of the power grid are necessary in aspects of safety and stability analysis of the power grid, safety weak link discovery and the like. With the continuous expansion of the interconnection scale of the power grid, the structure of the power grid becomes more and more complex, the real-time tracking and online analysis of the state of the power grid become more and more difficult, the online analysis and calculation of the existing complex power grid are usually completed on the basis of the simplification of the power grid, and a power grid equivalence method is a main means for the simplification of the power grid. The accuracy of the power grid equivalence depends on the effectiveness of a parameter identification method in the power grid equivalence model.
The existing power grid equivalent model parameter identification method generally identifies power grid equivalent model parameters by using steady-state electric quantity reflected by measurement data of a power grid in different running states, and the identification method has the contradiction between parameter identifiability and parameter change, namely, the parameters of the power grid equivalent model are changed along with factors such as power supply or power grid load change and power grid topological structure change, so that the change of the power grid equivalent model parameters needs to be tracked in real time in the parameter identification process. However, in a normal state, the change of the power grid operation state is smooth, so that the difference of the measured steady-state electric quantity data is not obvious, and the identification of model parameters cannot be realized; after the change of the operation condition of the power grid is enough to cause the obvious difference of the steady-state electric quantity data, the parameter to be identified of the model is changed, and the parameter identification cannot be realized by using the measured data on the premise of assuming that the parameter is not changed.
The method for realizing the tracking and identification of the equivalent parameters of the power grid based on the transient electric quantity generated by the disturbance of the power grid can solve the problems existing in the parameter identification based on the steady-state electric quantity, realizes the real-time tracking of the running state of the power grid, and is an important research direction of the power grid research. However, the existing power grid equivalent parameter identification based on the transient power has to collect power measurement data before and after the disturbance occurs, and the identification is established on the premise that the power grid parameters before and after the disturbance are not changed, so that the existing method is narrow in application range, and the transient power data is relatively complex to acquire.
Disclosure of Invention
The invention aims to provide a tracking and identifying method for equivalent parameters of a power grid, which realizes tracking and identifying of the equivalent parameters of the power grid by utilizing voltage, current and electric quantity in a power grid running state, and can perform multiple simple network equivalence on two sides of a port of a power network to be equivalent, so that the parameter characteristics of the power grid running state can be tracked, and an analysis basis can be provided for static stability and dynamic stability judgment of the power grid.
In order to solve the technical problem, the invention provides a power grid equivalent parameter tracking and identifying method, which comprises the following steps:
s1: extracting a voltage signal and a current signal at a first moment after disturbance and a voltage signal and a current signal at a second moment after disturbance from a port of a power network to be equalized, calculating voltage and current transient state electric quantity data according to the voltage signal and the current signal, establishing a voltage and current high-order differential equation at two sides of the port of the power network to be equalized and a voltage and current high-order differential equation of the whole power network to be equalized, stripping a voltage and current transient state electric quantity part from each established high-order differential equation, obtaining a voltage and current transient state electric quantity high-order differential equation at two sides of the port of the power network to be equalized and a voltage and current transient state electric quantity high-order differential equation of the whole power network to be equalized, and solving coefficients of each high-order differential equation according to the voltage and current transient state electric quantity data;
s2: stripping voltage and current steady state electric quantity parts from the established high-order differential equations to obtain voltage and current steady state electric quantity high-order differential equations at two sides of the port of the electric power network to be equalized, simplifying the voltage and current steady state electric quantity high-order differential equations at two sides of the port of the electric power network to be equalized to enable the voltage and current steady state electric quantity high-order differential equations to be consistent with the form of the electric network equivalent simple network differential equations at two sides of the port, associating the simplified steady state electric quantity high-order differential equations with corresponding coefficients of the electric network equivalent simple network differential equations, calculating electric network equivalent simple network parameters according to the coefficients of the high-order differential equations, and realizing tracking identification of the electric network equivalent parameters.
Further, the step S1 specifically includes:
s11: extracting a voltage signal u (t1) and a current signal i (t1) at the first time t1 and a voltage signal u (t2) and a current signal i (t2) at the second time t2 after a disturbance occurs from the grid; when the t2 is different from the t1 by one cycle, subtracting the voltage signal u (t1) and the current signal i (t1) after the disturbance occurs from the voltage signal u (t2) and the current signal i (t2) after the disturbance occurs; or when the difference between t2 and t1 is half a cycle, adding the voltage signal u (t2) and the current signal i (t2) after the disturbance occurs to the voltage signal u (t1) and the current signal i (t1) after the disturbance occurs to obtain a transient voltage signal Δ u (t) and a transient current signal Δ i (t);
s12: establishing a voltage-current high-order differential equation at two sides of a port of the power network to be equivalent:
and a voltage and current high-order differential equation of the whole power network to be equivalent:
wherein K is the order of the high order differential equation, u (t)(k)And i (t)(k)Is k-order derivative of port voltage signal and current signal, e (t) is equivalent power source of power network to be equivalent at right end of port,
an equivalent power supply of the power network to be equivalent at the left end of the port, akAnd bkThe high-order differential equation coefficient to be solved of the power network to be equivalent at the right end,
and
a high-order differential equation coefficient to be solved of the power network to be equivalent at the left end is represented by t, wherein K is 0, … and K;
here, the voltage and current signals of the port are composed of voltage and current steady-state signals and voltage and current transient signals, i.e.
Wherein u iss(t)、is(t) is a steady state voltage signal and a steady state current signal;
substituting the expression (4) into the expressions (1), (2) and (3) to obtain a voltage current steady-state electric quantity high-order differential equation:
and a voltage current transient state electric quantity high-order differential equation:
s13: according to the voltage and current transient state electric quantity data of S11, solving the coefficient a of the transient state electric quantity high-order differential equation of the formulas (8), (9) and (10) by adopting a least square methodk、bkAnd
further, step S2 specifically includes:
s21: will be provided with
Substituting the voltage current steady state electric quantity high-order differential equation at the right side of the port of the equation (5) to obtain:
the two sides of the formula (11) are simplified and combined to obtain
When K is an even number, let N be K/2, N be 0, …, N, and obtain:
when K is an odd number, let N be (K-1)/2, N be 0, …, N, and then:
s22: the power grid equivalent simple network differential equation of the power network to be equivalent on the right side of the port is set as follows:
wherein K 'is the order of the power grid equivalent simple network differential equation, obviously K'<K，us(t)(k)And is(t)(k)Is k order derivative of the port voltage steady state signal and the current steady state signal, eeq(t) is an equivalent power source a 'of the equivalent simple network of the right-end power grid'kAnd b'kThe coefficient of the equivalent simple network differential equation of the power grid is shown, t is time, and K is 0, … and K'; will be provided with
Substituting the equation (17) into the port right side power grid equivalent simple network differential equation to obtain:
by simply combining the two sides of formula (18), the product can be obtained
When K ' is an even number, let N ═ K '/2, N ═ 0, …, N ', we can find:
when K 'is an odd number, let N ═ 1)/2, N ═ 0, …, N', we can find:
s23: and (4) correlating the corresponding coefficients in the formula (12) in the step S21 and the formula (19) in the step S22, and calculating and solving equivalent simple network parameters according to the coefficients of the high-order differential equation to realize the tracking identification of the equivalent parameters of the power grid on the right side of the port.
S24: will be provided with
And substituting the voltage and current steady-state electric quantity high-order differential equation into the port left side voltage and current steady-state electric quantity high-order differential equation in the formula (6), and adopting the same methods of S21, S22 and S23 to realize the tracking identification of the equivalent parameters of the port left side power grid.
The invention has the beneficial effects that: the invention realizes the tracking identification of the equivalent parameters of the power grid by utilizing the voltage, current and electric quantity in the running state of the power grid, and can carry out multiple simple network equivalence on two sides of the port of the power network to be equivalent, thereby tracking the parameter characteristics of the running state of the power grid and providing an analysis basis for the static stability and dynamic stability judgment of the power grid. The method is completely based on the voltage, current and electric quantity of a power grid in the running state, so that data measurement is simplified, and the additional condition that the equivalent parameters are not changed before and after disturbance does not need to be observed.
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The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
FIG. 1 is a diagram of an electric power network with waiting equivalence
FIG. 2 is a circuit diagram of a Thevenin equivalent model according to an embodiment of the present invention;
FIG. 3 is a circuit diagram of a Norton equivalent model according to an embodiment of the present invention;
FIG. 4 is a circuit diagram of a generic equivalent model according to an embodiment of the present invention.
Detailed Description
A power grid equivalent parameter tracking and identifying method comprises the following steps:
s1: extracting a voltage signal and a current signal at a first moment after disturbance and a voltage signal and a current signal at a second moment after disturbance from a port of the power network to be equalized, which are shown in FIG. 1, calculating voltage and current transient state electric quantity data according to the voltage signal and the current signal, establishing a voltage and current high-order differential equation at two sides of the port of the power network to be equalized and a voltage and current high-order differential equation of the whole power network to be equalized, stripping a voltage and current transient state electric quantity part from each established high-order differential equation, obtaining the voltage and current transient state electric quantity high-order differential equation at two sides of the port of the power network to be equalized and the voltage and current transient state electric quantity high-order differential equation of the whole power network to be equalized, and solving coefficients of each high-order differential equation according to the voltage and current transient state electric quantity data;
s2: stripping voltage and current steady state electric quantity parts from the established high-order differential equations to obtain voltage and current steady state electric quantity high-order differential equations at two sides of the port of the electric power network to be equalized, simplifying the voltage and current steady state electric quantity high-order differential equations at two sides of the port of the electric power network to be equalized to enable the voltage and current steady state electric quantity high-order differential equations to be consistent with the form of the electric network equivalent simple network differential equations at two sides of the port, associating the simplified steady state electric quantity high-order differential equations with corresponding coefficients of the electric network equivalent simple network differential equations, calculating electric network equivalent simple network parameters according to the coefficients of the high-order differential equations, and realizing tracking identification of the electric network equivalent parameters.
Wherein, the step S1 specifically includes:
s11: for the power network to be equalized shown in fig. 1, the power network to be equalized includes power networks to be equalized on the left and right sides of a port; extracting from the port the voltage signal u (t1) and the current signal i (t1) at said first instant t1 and the voltage signal u (t2) and the current signal i (t2) at said second instant t2 after the occurrence of the disturbance; when the t2 is different from the t1 by one cycle, subtracting the voltage signal u (t1) and the current signal i (t1) after the disturbance occurs from the voltage signal u (t2) and the current signal i (t2) after the disturbance occurs; or when the difference between t2 and t1 is half a cycle, adding the voltage signal u (t2) and the current signal i (t2) after the disturbance occurs to the voltage signal u (t1) and the current signal i (t1) after the disturbance occurs to obtain a transient voltage signal Δ u (t) and a transient current signal Δ i (t);
s12: establishing a voltage-current high-order differential equation at two sides of a port of the power network to be equivalent:
and a voltage and current high-order differential equation of the whole power network to be equivalent:
wherein K is the order of the high order differential equation, u (t)(k)And i (t)(k)Is k-order derivative of port voltage signal and current signal, e (t) is equivalent power source of right-end equivalent power network,
for the equivalent power supply of the left-end standby equivalent power network, akAnd bkThe high-order differential equation coefficient to be solved of the power network to be equivalent at the right end,
and
a high-order differential equation coefficient to be solved of the power network to be equivalent at the left end is represented by t, wherein K is 0, … and K;
here, the voltage and current signals of the port are composed of voltage and current steady-state signals and voltage and current transient signals, i.e.
Wherein u iss(t)、is(t) is stableA steady state voltage signal and a steady state current signal.
Substituting the expression (4) into the expressions (1), (2) and (3) to obtain a voltage current steady-state electric quantity high-order differential equation:
and a voltage current transient state electric quantity high-order differential equation:
s13: according to the voltage and current transient state electric quantity data of S11, solving the coefficient a of the transient state electric quantity high-order differential equation of the formulas (8), (9) and (10) by adopting a least square methodk、bkAnd
the step S2 specifically includes:
s21: will be provided with
Substituting the voltage and current steady state electric quantity high-order differential equation on the right side of the port in the formula (5) to obtain：
The two sides of the formula (11) are simplified and combined to obtain
When K is an even number, let N be K/2, N be 0, …, N, and obtain:
when K is an odd number, let N be (K-1)/2, N be 0, …, N, and then:
s22: the equivalent simple network differential equation of the power grid on the right side of the port is set as follows:
wherein K 'is the order of the power grid equivalent simple network differential equation, obviously K'<K，us(t)(k)And is(t)(k)Is k order derivative of the port voltage steady state signal and the current steady state signal, eeq(t) is an equivalent power source a 'of the equivalent simple network of the right-end power grid'kAnd b'kThe coefficient of the equivalent simple network differential equation of the power grid is shown, t is time, and K is 0, … and K'; will be provided with
Substituting the equation (17) into the port right side power grid equivalent simple network differential equation to obtain:
by simply combining the two sides of formula (18), the product can be obtained
When K ' is an even number, let N ═ K '/2, N ═ 0, …, N ', we can find:
when K 'is an odd number, let N ═ 1)/2, N ═ 0, …, N', we can find:
s23: correlating the corresponding coefficients in the formula (12) in the step S21 and the formula (19) in the step S22, calculating and solving equivalent simple network parameters according to the coefficients of the high-order differential equation, and realizing the tracking identification of the equivalent parameters of the power grid on the right side of the port; if the number of the power grid equivalent simple network parameters is less than 4, the power grid equivalent simple network parameters can be uniquely solved, and if the number of the power grid equivalent simple network parameters is more than 4, the power grid equivalent simple network parameters have multiple groups of solutions.
S24: will be provided with
Substituting the voltage and current steady-state electric quantity high-order differential equation of the left side of the port in the formula (6), and adopting the same methods of S21, S22 and S23 to realize the tracking identification of equivalent parameters of the left side of the port; if the number of the power grid equivalent simple network parameters is less than 4, the power grid equivalent simple network parameters can be uniquely solved, and if the number of the power grid equivalent simple network parameters is more than 4, the power grid equivalent simple network parameters have multiple groups of solutions.
Specific applications of the above-described method are specifically exemplified below.
Example 1
The power network shown in fig. 2 is used as a power network to be equalized, a voltage-current transient state electric quantity high-order differential equation of the power network to be equalized is obtained through the method step S1, and each order derivative Δ u (t) of the transient state electric quantity is obtained through a numerical method(k)、Δi(t)(k)Solving the coefficient a of the higher order differential equation by using a least square methodk、bk(ii) a The high-order differential equation of the voltage and current steady-state electric quantity at two sides of the power network port to be equalized is obtained through the method step S2, the high-order differential equation of the voltage and current steady-state electric quantity at two sides of the power network port to be equalized is simplified, and four parameters A under the steady-state condition can be obtained through the formula (12) in S210、A1、B0、B1。
From thevenin's theorem, for any port power network, the voltage-current characteristics of the power network port can be characterized in the form of a power source series impedance (as shown in fig. 2). The Thevenin equivalent network differential equation under the steady state is obtained from FIG. 2:
will be provided with
Substituting formula (24) to obtain:
in comparison with formula (19), it is found that: a'0＝1、A′1＝0、B′0＝Req、B′1＝ωLeq. The formula (12) is converted into a form consistent with the equivalent simple network differential equation (25) of the power grid by adopting mathematical transformation to obtain
And then, correlating the simplified high-order differential equation (26) with a corresponding coefficient of the power grid equivalent simple network differential equation (25), and solving equivalent simple network parameters to obtain Thevenin equivalent parameters:
according to the voltage and current values measured by the power network port, the Thevenin equivalent power supply can be obtained by using the formula (25)
And completing the tracking identification of the Thevenin equivalent network parameters of the power grid.
Example 2
As shown in fig. 3, the power network to be equalized is a power network to be equalized, and as known from norton's theorem, for any port power network, it can be equivalently modeled as a current source parallel reactance (as shown in fig. 3), and a norton's equivalent network differential equation in a steady state is obtained from fig. 3:
will be provided with
Substituting formula (24) to obtain:
in comparison with formula (19), it is found that: a'0＝1/Req、A′1＝ωCeq、B′0＝1、B′10. The formula (12) is converted into a form consistent with the equivalent simple network differential equation (29) of the power grid by adopting mathematical transformation, and the result is obtained
Then, the simplified high-order differential equation (30) is associated with the corresponding coefficient of the equivalent simple network differential equation (29) of the power grid, and the equivalent simple network parameters are solved to obtain
According to the voltage and current values measured by the power network port, the Noton equivalent power supply can be obtained by using the formula (29)
And completing the tracking identification of the network parameters of the power grid Noton equivalent.
Example 3
As shown in fig. 4, the power network is used as a power network to be equivalent, in an actual power grid equivalent method, a complex system is further equivalent to a model (as shown in fig. 4) in which a resistance series inductance is added with a capacitance to ground, and an equivalent network differential equation in a steady state of the embodiment 3 is obtained from fig. 4:
will be provided with
Substituting formula (32) to obtain:
correlating the simplified differential equation (12) with the corresponding coefficient of the equivalent simple network differential equation (33) of the power grid, and solving the equivalent simple network parameters to obtain
The equivalent power source of example 3 can be obtained from the voltage and current values measured at the power network port by using equation (33)
And completing the tracking identification of the equivalent network parameters in example 3.
The method can theoretically solve the equivalent parameters of different equivalent models under the condition that the number of the to-be-equivalent power network parameters is less than or equal to 4. The method can track and identify parameters aiming at various equivalent power network models.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.
Claims (1)
1. A power grid equivalent parameter tracking and identifying method is characterized by comprising the following steps:
s1: extracting a voltage signal and a current signal at a first moment after disturbance and a voltage signal and a current signal at a second moment after disturbance from a port of a power network to be equalized, calculating voltage and current transient state electric quantity data according to the voltage signal and the current signal, establishing a voltage and current high-order differential equation at two sides of the port of the power network to be equalized and a voltage and current high-order differential equation of the whole power network to be equalized, stripping a voltage and current transient state electric quantity part from each established high-order differential equation, obtaining a voltage and current transient state electric quantity high-order differential equation at two sides of the port of the power network to be equalized and a voltage and current transient state electric quantity high-order differential equation of the whole power network to be equalized, and solving coefficients of each high-order differential equation according to the voltage and current transient state electric quantity data;
s2: stripping a voltage and current steady state electric quantity part from each established high-order differential equation to obtain voltage and current steady state electric quantity high-order differential equations at two sides of a port of the electric power network to be equivalent, simplifying the voltage and current steady state electric quantity high-order differential equations at two sides of the port of the electric power network to be equivalent so as to be consistent with the form of the electric network equivalent simple network differential equations at two sides of the port, associating the simplified steady state electric quantity high-order differential equations with corresponding coefficients of the electric network equivalent simple network differential equations, calculating electric network equivalent simple network parameters according to the coefficients of the high-order differential equations, and realizing tracking identification of the electric network equivalent parameters;
wherein, the step S1 specifically includes:
s11: extracting a voltage signal u (t1) and a current signal i (t1) at the first time t1 and a voltage signal u (t2) and a current signal i (t2) at the second time t2 after a disturbance occurs from the grid; when the t2 is different from the t1 by one cycle, subtracting the voltage signal u (t1) and the current signal i (t1) after the disturbance occurs from the voltage signal u (t2) and the current signal i (t2) after the disturbance occurs; or when the difference between t2 and t1 is half a cycle, adding the voltage signal u (t2) and the current signal i (t2) after the disturbance occurs to the voltage signal u (t1) and the current signal i (t1) after the disturbance occurs to obtain a transient voltage signal Δ u (t) and a transient current signal Δ i (t);
s12: establishing a voltage-current high-order differential equation at two sides of a port of the power network to be equivalent:
and a voltage and current high-order differential equation of the whole power network to be equivalent:
wherein K is the order of the high order differential equation, u (t)(k)And i (t)(k)Is k-order derivative of port voltage signal and current signal, e (t) is equivalent power source of power network to be equivalent at right end of port,
an equivalent power supply of the power network to be equivalent at the left end of the port, akAnd bkThe high-order differential equation coefficient to be solved of the power network to be equivalent at the right end,
and
a high-order differential equation coefficient to be solved of the power network to be equivalent at the left end is represented by t, wherein K is 0, … and K;
here, the voltage and current signals of the port are composed of voltage and current steady-state signals and voltage and current transient signals, i.e.
Wherein u iss(t)、is(t) is a steady state voltage signal and a steady state current signal;
substituting the expression (4) into the expressions (1), (2) and (3) to obtain a voltage current steady-state electric quantity high-order differential equation:
and a voltage current transient state electric quantity high-order differential equation:
s13: according to the voltage and current transient state electric quantity data of S11, solving the coefficient a of the transient state electric quantity high-order differential equation of the formulas (8), (9) and (10) by adopting a least square methodk、bkAnd
further, step S2 specifically includes:
s21: will be provided with
Substituting into the port of formula (5)And (3) obtaining a high-order differential equation of the steady-state electric quantity of the voltage and the current on the right side:
the two sides of the formula (11) are simplified and combined to obtain
When K is an even number, let N be K/2, N be 0, …, N, and obtain:
when K is an odd number, let N be (K-1)/2, N be 0, …, N, and then:
s22: the power grid equivalent simple network differential equation of the power network to be equivalent on the right side of the port is set as follows:
wherein K 'is the order of the power grid equivalent simple network differential equation, obviously K'<K，us(t)(k)And is(t)(k)Is k order derivative of the port voltage steady state signal and the current steady state signal, eeq(t) is an equivalent power source a 'of the equivalent simple network of the right-end power grid'kAnd b'kThe coefficient of the equivalent simple network differential equation of the power grid is shown, t is time, and K is 0, … and K'; will be provided with
Substituting the equation (17) into the port right side power grid equivalent simple network differential equation to obtain:
by simply combining the two sides of formula (18), the product can be obtained
When K ' is an even number, let N ═ K '/2, N ═ 0, …, N ', we can find:
when K 'is an odd number, let N ═ 1)/2, N ═ 0, …, N', we can find:
s23: correlating the corresponding coefficients in the formula (12) in the step S21 and the formula (19) in the step S22, calculating and solving equivalent simple network parameters according to the coefficients of the high-order differential equation, and realizing the tracking identification of the equivalent parameters of the power grid on the right side of the port;
s24: will be provided with
And substituting the voltage and current steady-state electric quantity high-order differential equation into the port left side voltage and current steady-state electric quantity high-order differential equation in the formula (6), and adopting the same methods of S21, S22 and S23 to realize the tracking identification of the equivalent parameters of the port left side power grid.
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