Electromagnetic transient simulation method and system based on discrete similarity principle
阅读说明：本技术 一种基于离散相似原理的电磁暂态仿真方法及系统 (Electromagnetic transient simulation method and system based on discrete similarity principle ) 是由 姚蜀军 宋文达 姚逸凡 汪燕 韩民晓 于 2020-06-16 设计创作，主要内容包括：本发明涉及一种基于离散相似原理的电磁暂态仿真方法及系统。该仿真方法包括：获取包含多节点的电力系统,并在节点分析法框架下,划分为组合元件以及独立元件；将RL并联件以及RC串联件分解成独立元件的形式,并对所有独立元件叠加虚拟电阻,确定重组的RL串联件以及重组的RC并联件；基于离散相似原理,确定重组的RL串联件差分方程以及重组的RC并联件差分方程,并确定RL串联件、RC并联件以及独立元件进行差分化处理,确定RL串联件差分方程、RC并联件差分方程以及独立元件差分方程；根据上述所有的差分方程对电力系统进行迭代仿真,得到电力系统的电磁暂态仿真结果。采用该仿真方法或系统能够对独立电感和电容进行仿真且能够抑制非原型数值振荡。(The invention relates to an electromagnetic transient simulation method and system based on a discrete similarity principle. The simulation method comprises the following steps: acquiring a power system comprising multiple nodes, and dividing the power system into a combined element and an independent element under a node analysis method framework; decomposing the RL parallel connection piece and the RC series connection piece into the form of independent elements, superposing virtual resistors on all the independent elements, and determining a recombined RL series connection piece and a recombined RC parallel connection piece; determining a recombined RL series element differential equation and a recombined RC parallel element differential equation based on a discrete similarity principle, determining the RL series element, the RC parallel element and the independent element to perform differential processing, and determining the RL series element differential equation, the RC parallel element differential equation and the independent element differential equation; and performing iterative simulation on the power system according to all the difference equations to obtain an electromagnetic transient simulation result of the power system. The simulation method or the simulation system can simulate the independent inductor and the independent capacitor and can inhibit the non-prototype numerical oscillation.)
1. An electromagnetic transient simulation method based on a discrete similarity principle is characterized by comprising the following steps:
acquiring a power system comprising multiple nodes, and dividing the power system into a combined element and an independent element under a node analysis method framework; the combination element comprises an RL series piece, an RL parallel piece, an RC series piece and an RC parallel piece; the independent elements comprise a resistor R, an inductor L and a capacitor C;
decomposing the RL parallel connection piece and the RC series connection piece into the form of independent elements, and superposing virtual resistors on all the independent elements to determine a recombined RL series connection piece and a recombined RC parallel connection piece;
based on a discrete similarity principle, respectively carrying out differential processing on the recombined RL series element and the recombined RC parallel element, and determining a recombined RL series element differential equation and a recombined RC parallel element differential equation;
determining the RL series connection element, the RC parallel connection element and the independent element to carry out differencing processing according to the recombined RL series connection element differential equation and the recombined RC parallel connection element differential equation, and determining an RL series connection element differential equation, an RC parallel connection element differential equation and an independent element differential equation;
performing iterative simulation on the electric power system according to the recombined RL series element differential equation, the recombined RC parallel element differential equation, the recombined RL series element differential equation, the recombined RC parallel element differential equation and the independent element differential equation to obtain an electromagnetic transient simulation result of the electric power system; and the electromagnetic transient simulation result is used for judging the stability of the power equipment.
2. The discrete similarity principle-based electromagnetic transient simulation method according to claim 1, wherein the decomposing of the combined elements into the form of independent elements and the superimposing of virtual resistances for all the independent elements, determining a recombined RL series connection and a recombined RC parallel connection, specifically comprises:
connecting an inductor which is decomposed into independent elements in series with a positive resistor and a negative resistor to determine a recombined RL series connection element;
a positive resistance and a negative resistance are connected in parallel to the capacitor decomposed into independent elements, and the recombined RC parallel connection piece is determined.
3. The discrete similarity principle-based electromagnetic transient simulation method according to claim 1, wherein the discrete similarity principle-based differencing the re-assembled RL series element and the re-assembled RC parallel element respectively to determine a re-assembled RL series element differential equation and a re-assembled RC parallel element differential equation specifically comprises:
acquiring a time domain state equation of a target element; the target element is the recombined RL series or the recombined RC parallel;
performing Laplace transformation on the time domain state equation to determine a transfer function of the continuous system;
determining a zero and a pole of the continuous system according to the transfer function of the continuous system;
determining the zero and the pole of the discrete system according to the zero and the pole of the continuous system based on a zero-pole response matching method;
constructing a transfer function of the discrete system according to the zero and the pole of the discrete system;
determining a difference equation according to the transfer function of the discrete system; the difference equation is a recombined RL series element difference equation or a recombined RC parallel element difference equation.
4. The discrete similarity principles-based electromagnetic transient simulation method according to claim 3, wherein the constructing a transfer function of a discrete system from the zeros and poles of the discrete system further comprises:
respectively constructing a final value of the transfer function of the continuous system and a final value of the transfer function of the discrete system based on a final value theorem;
and determining a gain value according to the final value of the transfer function of the continuous system and the final value of the transfer function of the discrete system.
5. The discrete similarity principle-based electromagnetic transient simulation method according to claim 4, wherein the determining a difference equation according to the transfer function of the discrete system specifically comprises:
and performing z-inverse transformation processing on the transfer function of the discrete system to determine a difference equation.
6. An electromagnetic transient simulation system based on discrete similarity principles, comprising:
the system comprises a dividing module, a judging module and a judging module, wherein the dividing module is used for acquiring a power system comprising multiple nodes and dividing the power system into a combined element and an independent element under a node analysis method framework; the combination element comprises an RL series piece, an RL parallel piece, an RC series piece and an RC parallel piece; the independent elements comprise a resistor R, an inductor L and a capacitor C;
the virtual resistance superposition module is used for decomposing the RL parallel connection piece and the RC series connection piece into the form of independent elements, superposing virtual resistance on all the independent elements and determining a recombined RL series connection piece and a recombined RC parallel connection piece;
the first difference processing module is used for respectively carrying out difference processing on the recombined RL series element and the recombined RC parallel element based on a discrete similarity principle, and determining a recombined RL series element difference equation and a recombined RC parallel element difference equation;
the second difference processing module is used for determining the RL series element, the RC parallel element and the independent element to carry out difference processing according to the recombined RL series element difference equation and the recombined RC parallel element difference equation, and determining the RL series element difference equation, the RC parallel element difference equation and the independent element difference equation;
the electric power system simulation module is used for carrying out iterative simulation on the electric power system according to the recombined RL series element differential equation, the recombined RC parallel element differential equation, the recombined RL series element differential equation, the recombined RC parallel element differential equation and the independent element differential equation to obtain an electromagnetic transient simulation result of the electric power system; and the electromagnetic transient simulation result is used for judging the stability of the power equipment.
7. The discrete similarity principle-based electromagnetic transient simulation system according to claim 6, wherein the virtual resistance superposition module specifically comprises:
a recombined RL series element determination unit for determining recombined RL series elements by connecting a positive resistance and a negative resistance in series to the inductor decomposed into independent elements;
and the recombined RC parallel connection piece determining unit is used for connecting a positive resistor and a negative resistor in parallel to the capacitor decomposed into independent elements to determine the recombined RC parallel connection piece.
8. The discrete similarity principle-based electromagnetic transient simulation system according to claim 6, wherein the first differencing processing module specifically includes:
the time domain state equation obtaining unit is used for obtaining a time domain state equation of the target element; the target element is the recombined RL series or the recombined RC parallel;
the transfer function determining unit of the continuous system is used for performing Laplace transformation on the time domain state equation to determine the transfer function of the continuous system;
a zero and pole determination unit of the continuous system, for determining the zero and pole of the continuous system according to the transfer function of the continuous system;
the zero and pole determining unit of the discrete system is used for determining the zero and the pole of the discrete system according to the zero and the pole of the continuous system based on a zero and pole response matching method;
the transfer function constructing unit of the discrete system is used for constructing the transfer function of the discrete system according to the zero and the pole of the discrete system;
the differential equation determining unit is used for determining a differential equation according to the transfer function of the discrete system; the difference equation is a recombined RL series element difference equation or a recombined RC parallel element difference equation.
9. The discrete similarity principles-based electromagnetic transient simulation system of claim 8, further comprising:
a final value determining unit configured to construct a final value of the transfer function of the continuous system and a final value of the transfer function of the discrete system, respectively, based on a final value theorem;
a gain value determining unit, configured to determine a gain value according to the final value of the transfer function of the continuous system and the final value of the transfer function of the discrete system.
10. The discrete similarity principle-based electromagnetic transient simulation system according to claim 9, wherein the differential equation determination unit specifically comprises:
and the difference equation determining subunit is used for performing z inverse transformation processing on the transfer function of the discrete system to determine a difference equation.
Technical Field
The invention relates to the field of electromagnetic transient simulation, in particular to an electromagnetic transient simulation method and system based on a discrete similarity principle.
Background
With the development of high voltage Direct current transmission (HVDC), Flexible Alternating Current Transmission (FACTS) and large-scale new energy, a large number of power electronic devices are connected to a power grid, so that the current power system shows a power electronization trend. The power electronic device has the characteristics of high action frequency and fast transient process, which provides a new challenge for electromagnetic transient simulation. The performance of electromagnetic transient simulation is influenced by the selection and design of the numerical integration algorithm, and whether the simulation precision can be improved and the numerical oscillation can be inhibited is an important factor for measuring the performance of the numerical integration algorithm.
The performance of electromagnetic transient simulation is influenced by the selection and design of a numerical integration algorithm, and most of the traditional electromagnetic transient numerical integration methods are based on a time domain approximation method. In the numerical integration method based on the time domain approximation method, the implicit trapezoidal method is widely used due to the second-order precision and the A-stability, but the numerical oscillation problem exists when the network topology changes in the algorithm. The back-off euler method can effectively suppress the problem of numerical oscillation of the implicit trapezoidal method, but the back-off euler method adopts a rectangular area to approximately replace the curved-edge area of the integral and only has first-order precision. In order to solve the problems, the critical damping method fuses the two methods, and after the switch is operated, the implicit trapezoidal method is switched into a two-step half-step backward Euler method to restrain the non-prototype numerical oscillation. However, the problem of low precision of the backward euler method is still not solved, and on the other hand, the method needs to design an algorithm switching function for all elements, so that a new problem of complicated programming occurs.
The root matching method directly constructs a discrete system similar to the continuous system from the angle that the essence of simulation is the discretization process of the continuous system, thereby realizing the simulation of the continuous system. However, this method has a problem that the independent inductance and capacitance elements cannot be differentiated, and cannot effectively suppress the non-prototype numerical oscillation.
Disclosure of Invention
The invention aims to provide an electromagnetic transient simulation method and system based on a discrete similarity principle, and aims to solve the problems that the existing electromagnetic transient simulation method cannot be suitable for independent inductors and capacitors and cannot effectively inhibit numerical oscillation of a non-prototype.
In order to achieve the purpose, the invention provides the following scheme:
an electromagnetic transient simulation method based on a discrete similarity principle comprises the following steps:
acquiring a power system comprising multiple nodes, and dividing the power system into a combined element and an independent element under a node analysis method framework; the combination element comprises an RL series piece, an RL parallel piece, an RC series piece and an RC parallel piece; the independent elements comprise a resistor R, an inductor L and a capacitor C;
decomposing the RL parallel connection piece and the RC series connection piece into the form of independent elements, and superposing virtual resistors on all the independent elements to determine a recombined RL series connection piece and a recombined RC parallel connection piece;
based on a discrete similarity principle, respectively carrying out differential processing on the recombined RL series element and the recombined RC parallel element, and determining a recombined RL series element differential equation and a recombined RC parallel element differential equation;
determining the RL series connection element, the RC parallel connection element and the independent element to carry out differencing processing according to the recombined RL series connection element differential equation and the recombined RC parallel connection element differential equation, and determining an RL series connection element differential equation, an RC parallel connection element differential equation and an independent element differential equation;
performing iterative simulation on the electric power system according to the recombined RL series element differential equation, the recombined RC parallel element differential equation, the recombined RL series element differential equation, the recombined RC parallel element differential equation and the independent element differential equation to obtain an electromagnetic transient simulation result of the electric power system; and the electromagnetic transient simulation result is used for judging the stability of the power equipment.
Optionally, the decomposing the combination element into a form of independent elements, and superimposing a virtual resistance on all the independent elements to determine a recombined RL series component and a recombined RC parallel component specifically include:
connecting an inductor which is decomposed into independent elements in series with a positive resistor and a negative resistor to determine a recombined RL series connection element;
a positive resistance and a negative resistance are connected in parallel to the capacitor decomposed into independent elements, and the recombined RC parallel connection piece is determined.
Optionally, the performing difference processing on the recombined RL series element and the recombined RC parallel element respectively based on the discrete similarity principle to determine a recombined RL series element difference equation and a recombined RC parallel element difference equation specifically includes:
acquiring a time domain state equation of a target element; the target element is the recombined RL series or the recombined RC parallel;
performing Laplace transformation on the time domain state equation to determine a transfer function of the continuous system;
determining a zero and a pole of the continuous system according to the transfer function of the continuous system;
determining the zero and the pole of the discrete system according to the zero and the pole of the continuous system based on a zero-pole response matching method;
constructing a transfer function of the discrete system according to the zero and the pole of the discrete system;
determining a difference equation according to the transfer function of the discrete system; the difference equation is a recombined RL series element difference equation or a recombined RC parallel element difference equation.
Optionally, the constructing a transfer function of the discrete system according to the zero and the pole of the discrete system further includes:
respectively constructing a final value of the transfer function of the continuous system and a final value of the transfer function of the discrete system based on a final value theorem;
and determining a gain value according to the final value of the transfer function of the continuous system and the final value of the transfer function of the discrete system.
Optionally, the determining a difference equation according to the transfer function of the discrete system specifically includes:
and performing z-inverse transformation processing on the transfer function of the discrete system to determine a difference equation.
An electromagnetic transient simulation system based on discrete similarity principles, comprising:
the system comprises a dividing module, a judging module and a judging module, wherein the dividing module is used for acquiring a power system comprising multiple nodes and dividing the power system into a combined element and an independent element under a node analysis method framework; the combination element comprises an RL series piece, an RL parallel piece, an RC series piece and an RC parallel piece; the independent elements comprise a resistor R, an inductor L and a capacitor C;
the virtual resistance superposition module is used for decomposing the RL parallel connection piece and the RC series connection piece into the form of independent elements, superposing virtual resistance on all the independent elements and determining a recombined RL series connection piece and a recombined RC parallel connection piece;
the first difference processing module is used for respectively carrying out difference processing on the recombined RL series element and the recombined RC parallel element based on a discrete similarity principle, and determining a recombined RL series element difference equation and a recombined RC parallel element difference equation;
the second difference processing module is used for determining the RL series element, the RC parallel element and the independent element to carry out difference processing according to the recombined RL series element difference equation and the recombined RC parallel element difference equation, and determining the RL series element difference equation, the RC parallel element difference equation and the independent element difference equation;
the electric power system simulation module is used for carrying out iterative simulation on the electric power system according to the recombined RL series element differential equation, the recombined RC parallel element differential equation, the recombined RL series element differential equation, the recombined RC parallel element differential equation and the independent element differential equation to obtain an electromagnetic transient simulation result of the electric power system; and the electromagnetic transient simulation result is used for judging the stability of the power equipment.
Optionally, the virtual resistance superposition module specifically includes:
a recombined RL series element determination unit for determining recombined RL series elements by connecting a positive resistance and a negative resistance in series to the inductor decomposed into independent elements;
and the recombined RC parallel connection piece determining unit is used for connecting a positive resistor and a negative resistor in parallel to the capacitor decomposed into independent elements to determine the recombined RC parallel connection piece.
Optionally, the first difference processing module specifically includes:
the time domain state equation obtaining unit is used for obtaining a time domain state equation of the target element; the target element is the recombined RL series or the recombined RC parallel;
the transfer function determining unit of the continuous system is used for performing Laplace transformation on the time domain state equation to determine the transfer function of the continuous system;
a zero and pole determination unit of the continuous system, for determining the zero and pole of the continuous system according to the transfer function of the continuous system;
the zero and pole determining unit of the discrete system is used for determining the zero and the pole of the discrete system according to the zero and the pole of the continuous system based on a zero and pole response matching method;
the transfer function constructing unit of the discrete system is used for constructing the transfer function of the discrete system according to the zero and the pole of the discrete system;
the differential equation determining unit is used for determining a differential equation according to the transfer function of the discrete system; the difference equation is a recombined RL series element difference equation or a recombined RC parallel element difference equation.
Optionally, the method further includes:
a final value determining unit configured to construct a final value of the transfer function of the continuous system and a final value of the transfer function of the discrete system, respectively, based on a final value theorem;
a gain value determining unit, configured to determine a gain value according to the final value of the transfer function of the continuous system and the final value of the transfer function of the discrete system.
Optionally, the difference equation determining unit specifically includes:
and the difference equation determining subunit is used for performing z inverse transformation processing on the transfer function of the discrete system to determine a difference equation.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides an electromagnetic transient simulation method and system based on a discrete similarity principle, which solve the problem of differentiation of independent elements by using a method of superposing virtual positive and negative resistors. Because the inductance L and the capacitance C do not have poles, the difference of the inductance L and the capacitance C can not be directly carried out by using a zero pole response matching method, therefore, the discrete similarity method is not suitable for the L and the C.
Because the positive and negative virtual resistors are introduced simultaneously, the original circuit is not changed substantially, so that the stability problem is avoided, and the superposition of the positive and negative virtual resistors ensures that a discrete similarity method can simulate the independent element.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a schematic diagram of domain switching involved in different differencing methods of the present invention;
FIG. 2 is a flowchart of an electromagnetic transient simulation method based on the discrete similarity principle according to the present invention;
FIG. 3 is a schematic diagram of an RL series circuit according to the present invention;
FIG. 4 is a schematic diagram of the differencing preprocessing provided by the present invention;
FIG. 5 is a schematic circuit diagram of an RL series equivalent branch circuit provided by the present invention;
FIG. 6 is a schematic diagram of the differentiation of L and C provided by the present invention; fig. 6(a) is a schematic diagram of inductance differentiation processing provided by the present invention; FIG. 6(b) is a simplified schematic diagram of a series circuit provided by the present invention; FIG. 6(c) is a schematic diagram of the capacitance differentiation process provided by the present invention; FIG. 6(d) is a simplified schematic diagram of a parallel circuit provided by the present invention;
fig. 7 is a structural diagram of an electromagnetic transient simulation system based on the discrete similarity principle provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an electromagnetic transient simulation method and system based on a discrete similarity principle, which can simulate an independent inductor L and a capacitor C and can inhibit non-prototype numerical oscillation.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The invention adopts a zero-pole response matching method to differentiate the continuous system, and the method is rigorous and reliable in the aspect of constructing a z-domain discrete system according to the physical significance of a zero point, a pole and a final value of a transfer function. The idea of the pole-zero response matching method is as follows: firstly, s transformation is carried out on the continuous system to obtain an s-domain transfer function H(s) for describing the continuous system. And then constructing a transfer function H (z) of a z domain by matching zeros, poles and final values, wherein the matching of the zeros and the poles ensures that H (z) is similar to H(s) transient response characteristics, and the matching of the final values ensures that H (z) is similar to H(s) steady-state response characteristics, namely H (z) has similar response characteristics to H(s).
The differentiation of the traditional integration method is directly carried out in the time domain, and the differentiation of the discrete similarity principle adopting zero-pole response matching is returned to the time domain from the time domain through the frequency domain. The conversion of the domain involved in differencing using conventional integration and discrete similarity principles is shown in fig. 1.
Fig. 2 is a flowchart of an electromagnetic transient simulation method based on the discrete similarity principle, and as shown in fig. 2, an electromagnetic transient simulation method based on the discrete similarity principle includes:
step 201: acquiring a power system comprising multiple nodes, and dividing the power system into a combined element and an independent element under a node analysis method framework; the combination element comprises an RL series piece, an RL parallel piece, an RC series piece and an RC parallel piece; the individual elements include a resistor R, an inductor L, and a capacitor C.
Step 202: and decomposing the RL parallel connection piece and the RC series connection piece into the form of independent elements, and superposing virtual resistors on all the independent elements to determine a recombined RL series connection piece and a recombined RC parallel connection piece.
The
Step 203: and on the basis of a discrete similarity principle, respectively carrying out differential processing on the recombined RL series element and the recombined RC parallel element, and determining a recombined RL series element differential equation and a recombined RC parallel element differential equation.
The
The constructing of the transfer function of the discrete system according to the zero and the pole of the discrete system further comprises: respectively constructing a final value of the transfer function of the continuous system and a final value of the transfer function of the discrete system based on a final value theorem; and determining a gain value according to the final value of the transfer function of the continuous system and the final value of the transfer function of the discrete system.
The determining a difference equation according to the transfer function of the discrete system specifically includes: and performing z-inverse transformation processing on the transfer function of the discrete system to determine a difference equation.
Step 204: and determining the RL series connection element, the RC parallel connection element and the independent element to carry out differencing processing according to the recombined RL series connection element differential equation and the recombined RC parallel connection element differential equation, and determining the RL series connection element differential equation, the RC parallel connection element differential equation and the independent element differential equation.
Step 205: performing iterative simulation on the electric power system according to the recombined RL series element differential equation, the recombined RC parallel element differential equation, the recombined RL series element differential equation, the recombined RC parallel element differential equation and the independent element differential equation to obtain an electromagnetic transient simulation result of the electric power system; and the electromagnetic transient simulation result is used for judging the stability of the power equipment.
For the sake of understanding, taking the RL series branch shown in fig. 3 as a representative combined branch as an example, the specific steps based on the discrete similar simulation method will be described from the combined element and both aspects, respectively.
As shown in fig. 4, step one: under the framework of nodal analysis, the power system is divided into combined elements and independent elements.
Step two: differential preprocessing:
pretreatment of combined elements: the RL parallel connection and the RC series connection in the combined element are decomposed into R, L, C independent element forms for processing.
Pretreatment of independent elements: superposing a positive virtual resistor and a negative virtual resistor, and connecting a positive resistor and a negative resistor in series to the inductor; a positive resistor and a negative resistor are connected in parallel to the capacitor. The positive and negative resistance values are the same, and are defined as Ra in this patent.
Step three: the simulation method based on the discrete similarity principle differentiates the target elements:
according to the simulation preprocessing in the second step, the RL parallel connection, the RC series connection and the independent elements in the combined element are converted into the RL series connection and the RC parallel connection for differentiation.
1) And acquiring a state equation of the target element.
The time domain state equation of the RL series branch is as follows:
2) and determining H(s), and calculating a zero point and a pole point.
Performing a Laplace transform on equation (1):
h(s) no zero, poles are:
ω'p＝-R/L (3)
3) preliminary structure H (z).
Constructing H (z) according to pole-zero matching:
where the poles of H (z) are:
4) solving for H (z) gain Kz1。
Taking the input signal as a unit step signal u (t) ═ 1 (t):
the final values of H(s) and H (z) are determined according to the final value theorem:
equation (8) and equation (9) are made equal, i.e.:
5) and performing z inverse transformation on H (z) to obtain a difference equation.
Inverse z transform h (z):
i(t+Δt)＝u(t+Δt)/Req+Ihis(11)
where Req and Ihis the equivalent resistance and history terms:
Ihis＝e-ΔtR/Li(t) (13)
equation (11) is a difference equation of RL series based on the discrete similarity method, and fig. 5 is an equivalent branch after RL series differentiation.
Step four: and (5) performing differential post-processing.
The combination elements RL series and RC parallel do not have to be post-processed.
The elements differentiated in the form of independent elements (RL parallel, RC series and independent elements in the combined element) require post-processing, i.e. circuit simplification: simplifying the circuit formed by the Norton equivalent circuit and the negative resistance obtained in the fourth step to obtain a final inductance and capacitance difference equation and the Norton equivalent circuit, wherein the table 1 is a differential equation schematic table of four combined elements based on a discrete similarity method, and the table 2 is a differential equation table of independent elements based on the discrete similarity method, as shown in the tables 1 and 2.
TABLE 1
TABLE 2
The two tables are the results of the RL series-parallel connection, the RC series-parallel connection and the independent element R, L, C obtained after the steps one, two, three and four, and are the final results, and the correctness of the invention can be verified by programming the expressions in the tables (i.e. the step five).
Fig. 6 shows the steps of differentiating L and C by the discrete similarity method, in fig. 6, firstly, corresponding to the step two, the independent element differentiation preprocessing, secondly, corresponding to the step three, the target element differentiation is performed based on the discrete similarity principle, and thirdly, corresponding to the step four, the differentiation post-processing. In the figure, the expressions of equivalent resistances RRLeq and RRCeq after differentiation and history items IRLhis and IRChis are shown in table 1. The step III in the figure is simplified, the number of nodes of the independent element is not changed when the independent element is simulated by adopting a discrete similarity method under a node analysis framework, for an inductor, the Noton equivalent resistance is the series connection of RRLeq and-Ra, for a capacitor, the Noton equivalent resistance is the parallel connection of RRCeq and-Ra, and the history items of the two are the short-circuit current of the circuit. The difference equation for the individual elements L and C can also be written in the form of equation (11).
Step five: after the equivalent branch and the difference equation of each element are obtained, iterative simulation is carried out on a system formed by the elements until the simulation is finished.
The invention can effectively inhibit numerical value oscillation:
as can be seen from tables 1 and 2, the history terms of the difference equations formed by the discrete similarity method for RL series connection, RC parallel connection, L, C and R do not contain non-state variables, which indicates that the discrete similarity method can effectively suppress the non-prototype numerical oscillation in the above 5 element simulations. It can be further known that the discrete similarity method can effectively suppress the non-prototype numerical oscillation occurring in the circuit simulation process consisting of the above 5 elements without coupling, and compared with the EMTP method, the algorithm switching function does not need to be designed for each element, thereby simplifying the program complexity.
The invention solves the problem that the independent elements can not be differentiated:
since there are no poles for L and C, L and C cannot be differentiated directly by the pole-zero response matching method, and the discrete similarity method is not applicable to L and C from this viewpoint.
The invention respectively connects the positive and negative virtual resistors in series and in parallel before differentiating the L and the C, converts the L and the C into an RL series connection and an RC parallel connection and then differentiates the L and the C, so that the discrete similarity method can simulate the L and the C and can inhibit the non-prototype numerical oscillation. The positive and negative virtual resistance Ra value does not influence the simulation result of the discrete similarity method on the steady-state process, but the Ra value has a slight influence on the transient process because the Ra is related to a time constant, and the optimal value of the Ra is determined according to the size of the L/C in the simulation. In addition, because the positive and negative virtual resistors are introduced simultaneously, the original circuit is not changed substantially, and therefore the stability problem cannot be caused. The significance of the positive and negative virtual resistors is that the discrete similarity method can be used for simulating the independent elements, otherwise, the application of the discrete similarity method has great limitation.
The invention can also improve the simulation precision:
equations (15), (16) and (17) are difference equations formed by the RL series branch by adopting a backward Euler method, an implicit trapezoidal method and a discrete similarity method respectively.
And (3) performing Taylor expansion on two terms of coefficients on the right side of the equal sign of the formula (17):
comparing the first order terms in equations (18) and (19) with equation (15) it can be seen that the coefficients in the receding euler difference equation are a first order taylor approximation of the discrete similarity coefficients.
And (2) carrying out Taylor expansion on two coefficients on the right side of the equal sign of the formula (17) in another mode:
also, by comparing the first-order term in the equations (20) and (21) with the equation (16), the first-order coefficient of the trapezoidal method is a first-order Taylor approximation of the first-order coefficient of the discrete similarity method, and the second-order coefficient is mainly the first-order coefficient of the discrete similarity methodThe first order taylor approximation of (a), because the discrete similarity method uses the format of the euler method, the trapezoidal method is not completely equal to the first order approximation of its coefficients.
Similar conclusion can be obtained by adopting other integration algorithms and the discrete similarity method or taking other branches as examples, namely that the coefficient of the difference equation based on the time domain approximation integration algorithm is the low-order taylor approximation of the discrete similarity method (for example, the variable parameter rational equation fitting method is the third-order taylor approximation of the discrete similarity method), which shows that the precision of the discrete phase method is higher than that of the simulation method based on the time domain approximation.
Fig. 7 is a structural diagram of an electromagnetic transient simulation system based on the discrete similarity principle, which is provided by the present invention, and the electromagnetic transient simulation system based on the discrete similarity principle includes:
the
A virtual
The virtual
A first
The first
The invention also includes: a final value determining unit configured to construct a final value of the transfer function of the continuous system and a final value of the transfer function of the discrete system, respectively, based on a final value theorem; a gain value determining unit, configured to determine a gain value according to the final value of the transfer function of the continuous system and the final value of the transfer function of the discrete system.
The difference equation determining unit specifically includes: and the difference equation determining subunit is used for performing z inverse transformation processing on the transfer function of the discrete system to determine a difference equation.
And a
The electric power
According to the method, a discrete system similar to a continuous system is constructed in a frequency domain through zero-pole response matching, a difference equation is obtained through inverse transformation of the frequency domain discrete system, and a combined element form capable of effectively inhibiting numerical oscillation is obtained through analysis and comparison based on the principle of non-prototype numerical oscillation generation. For the independent inductance and capacitance which can not directly apply zero pole response matching for differentiation, the method is respectively solved by connecting positive and negative virtual resistors in series and in parallel. Finally, the problem of numerical value oscillation of all elements is solved, and meanwhile, the simulation precision is improved.
Based on the principle of discrete similarity, efficient electromagnetic transient simulation is utilized from a time domain to a frequency domain and then to the time domain.
The method of superposing virtual positive and negative resistors is utilized to solve the problem of differentiation of independent elements. Because the L and the C do not have poles, the L and the C cannot be differentiated by directly utilizing a pole-zero response matching method, and the discrete similarity method is not suitable for the L and the C from the viewpoint; before differentiating L and C, respectively connecting positive and negative virtual resistors in series and parallel, converting L and C into RL series and RC parallel forms, and then differentiating, so that the discrete similarity method can simulate L and C and inhibit non-prototype numerical oscillation; in addition, because the positive and negative virtual resistors are introduced simultaneously, the original circuit is not changed substantially, and therefore the stability problem cannot be caused; the significance of the positive and negative virtual resistors is that the discrete similarity method can be used for simulating the independent elements, otherwise, the application of the discrete similarity method has great limitation; the positive and negative virtual resistance Ra value does not influence the simulation result of the discrete similarity method on the steady-state process, but the Ra value has a slight influence on the transient process because the Ra is related to a time constant, and the optimal value of the Ra is determined according to the size of the L/C in the simulation.
The analysis comparison yields the element form capable of suppressing the numerical oscillation of the prototype. One of the main reasons for the generation of the non-prototype numerical oscillation is that when the network topology changes, the history items of the differential equations contain non-state variables. Analysis of Table 1 reveals that the history entries of the RL series and RC parallel differential equations contain no non-state variables, while the RL parallel and RC series contain non-state variables u (t) and i (t). Therefore, for the simulation method based on the discrete similarity principle, the RL parallel and the RC parallel are in the form of combined elements capable of effectively suppressing the non-prototype numerical oscillation, while the RL parallel and the RC series cannot be processed as a whole as the two combined elements, and L, C and R are processed separately as independent elements after decomposition. The independent element is also converted into two forms of RL series connection and RC parallel connection which can inhibit numerical value oscillation by superposing positive and negative virtual resistors.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
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