CN109635374A - A kind of short-circuit current calculation method and device based on Dynamic Phasors time domain method - Google Patents
A kind of short-circuit current calculation method and device based on Dynamic Phasors time domain method Download PDFInfo
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Abstract
The invention discloses a kind of short-circuit current calculation methods based on Dynamic Phasors time domain method, comprising: establishes the element dynamic phasor model for being suitable for three-phase alternating current system calculation of short-circuit current；Using trapezoidal integration method, the dynamic phasor model is converted into algebraic equation, obtains the conductance matrix of malfunctioning node；Triangle decomposition is carried out to the conductance matrix, electric current calculating is carried out to the circuit to break down using the formula obtained after triangle decomposition, solves the problems, such as that the short circuit current standard simplified practical calculation method computational accuracy that positions occur under short-circuit conditions near long-distance transmission line, series compensation capacitance etc. is insufficient.
Description
Technical Field
The application relates to the field of power grid planning and operation and power system simulation analysis, in particular to a short-circuit current calculation method based on a dynamic phasor time domain method, and also relates to a short-circuit current calculation device based on the dynamic phasor time domain method.
Background
The calculation of the short-circuit current is the conventional content of the analysis of the power system, and the calculation of the short-circuit current is required to be carried out for selecting electrical equipment, setting a relay protection fixed value of a conductor and the like. The simulation of the short circuit process in the power system relates to electromagnetic transient calculation, but because the actual power system is very large in scale, the calculation of the short circuit current by applying the existing electromagnetic transient calculation method faces very difficult. The purpose of calculating and standardizing the short-circuit current is to obtain the maximum or minimum short-circuit current of the system by a relatively simplified practical method, and also to consider the safety of equipment and save investment. At present, each standard at home and abroad adopts a simplified method to calculate the short-circuit current, and can generally meet the requirements of engineering calculation.
The short-circuit current calculation method comprises the short-circuit current alternating-current component initial value, the direct-current component attenuation time constant, the impact short-circuit current and the like. In the practical short-circuit current calculation method, the calculation of the initial value of the alternating current component is based on a phasor analysis method, the time domain integral problem of the electromagnetic transient process is converted into a power frequency steady-state circuit algebraic solving problem, and the calculation process of the short-circuit current is greatly simplified. However, the calculation result of the alternating current component of the short-circuit current obtained by the method is substantially a steady-state solution of the power frequency component of the short-circuit current. For a general power network, the short-circuit current can reach the maximum value of the power frequency component instantly after the fault occurs. However, when the system contains a series compensation or an ultra-long high-voltage alternating-current line, the fault current near the elements during short circuit presents an obvious transition process, and the steady state of the alternating-current component can be achieved through several or even more than ten cycles, so that the practical short-circuit current calculation method is not applicable any more. Therefore, the problem that the calculation accuracy of the short-circuit current standard simplified practical calculation method is insufficient under the condition of short circuit at positions such as the positions near a remote power transmission line and a series compensation capacitor in the prior art exists.
Disclosure of Invention
The application provides a short-circuit current calculation method based on a dynamic phasor time domain method, and solves the problem that a short-circuit current standard simplified practical calculation method is insufficient in calculation accuracy under the condition that short circuits occur at positions such as a remote power transmission line and the vicinity of a series compensation capacitor.
The application provides a short-circuit current calculation method based on a dynamic phasor time domain method, which comprises the following steps:
establishing an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating-current system;
converting the dynamic phasor model into an algebraic equation by using a trapezoidal integral method to obtain a conductance matrix of a fault node;
and performing triangular decomposition on the conductance matrix, and performing current calculation on the circuit with the fault by using a formula obtained after triangular decomposition.
Preferably, the establishing of the element dynamic phasor model suitable for the short-circuit current calculation of the three-phase alternating current system includes:
establishing a synchronous machine model, in particular, using a constant voltage sourceInternal impedance ZS＝Ra+jX″dThe dynamic phasor differential equation of the simulated synchronous motor is as follows. Wherein the content of the first and second substances,in order to be the generator terminal voltage,
the dynamic phasor model expression is as follows:
establishing an alternating current line model, wherein the dynamic phasor model expression is as follows:
the line can be equally divided into two or more sections, each section adopts the model, and the dynamic phasor of the three-phase symmetrical line still meets the positive, negative and zero sequence decoupling principle, so that for the zero sequence circuit of the line, the parameters are only replaced by zero sequence parameters;
establishing a transformer model, wherein the expression of a dynamic phasor model is as follows:
establishing a reactive compensation and load model, wherein the expression of a dynamic phasor model is as follows:
preferably, the converting the dynamic phasor model into an algebraic equation by using a trapezoidal integration method to obtain the conductance matrix of the fault node includes:
a trapezoidal integral method is used, a damping coefficient is introduced, the dynamic phasor model is arranged to obtain a conductance matrix, the form is as follows,
the application also provides a short-circuit current calculating device based on the dynamic phasor time domain method, which comprises the following steps:
the model establishing unit is used for establishing an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating-current system;
the conversion unit is used for converting the dynamic phasor model into an algebraic equation by using a trapezoidal integral method to obtain a conductance matrix of a fault node;
and the calculation unit is used for carrying out triangular decomposition on the conductance matrix and calculating the current of the circuit with the fault by using a formula obtained after the triangular decomposition.
According to the short-circuit current calculation method based on the dynamic phasor time domain method, the dynamic phasor model is established, the dynamic phasor model time domain simulation curve can envelop the electromagnetic transient simulation curve, and the problem that the calculation accuracy of the short-circuit current standard simplified practical calculation method is insufficient under the condition that short circuit occurs at positions near a remote power transmission line and a series compensation capacitor is solved.
Drawings
Fig. 1 is a short-circuit current calculation method based on a dynamic phasor time domain method according to an embodiment of the present application;
FIG. 2 is a schematic diagram of a voltage source according to an embodiment of the present application being short-circuited via a resistor;
FIG. 3 is a graph showing the relationship between the curves of the equations (2) and (5) according to an embodiment of the present application;
FIG. 4 is a lumped parameter line model to which embodiments of the present application relate;
fig. 5 is a three-winding transformer model considering an excitation branch according to an embodiment of the present application;
FIG. 6 is an inductive and capacitive compensation/load equivalent circuit according to an embodiment of the present application;
FIG. 7 is a flowchart of a procedure for calculating a short-circuit current by a dynamic phasor method according to an embodiment of the present application;
FIG. 8 is a schematic diagram of a point-to-grid extra-high voltage half-wavelength alternating current transmission model according to an embodiment of the present application;
FIG. 9 shows the current at a three-phase short circuit at a 300KM position according to an embodiment of the present application;
FIG. 10 shows the current in a three-phase short circuit at a 24KM position according to an embodiment of the present application;
fig. 11 is a short-circuit current calculation apparatus based on a dynamic phasor time domain method according to an embodiment of the present application.
Detailed Description
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. This application is capable of implementation in many different ways than those herein set forth and of similar import by those skilled in the art without departing from the spirit of this application and is therefore not limited to the specific implementations disclosed below.
Referring to fig. 1, fig. 1 is a method for calculating a short-circuit current based on a dynamic phasor time domain method according to an embodiment of the present application, and the method according to the embodiment of the present application is described in detail with reference to fig. 1.
And step S101, establishing an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating-current system.
Before establishing an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating-current system, analyzing a short-circuit current curve.
For the circuit shown in fig. 2, a constant ac voltage source u with an angular velocity ω is applied through a resistor R and an inductor L at t0When the time is short-circuited at 0, the instantaneous value equation is expressed by the formula (1), wherein p is a differential operator.
The short-circuit current analytic solution (t is more than or equal to 0) is
in the formula：τ＝L/R，γ＝arctan(ωL/R)。
the short-circuit current of formula (2) includes an alternating current component and a direct current component: the amplitude of the alternating current component is constant; the dc component gradually decays to zero with a time constant τ. When the voltage angle at the moment of the short circuit is equal to the impedance angle, the dc component is zero.
Converting formula (1) into a dynamic phasor equation
Wherein the power supply voltageFor constant phasors, Laplace transform is applied, and side values are taken into accountUnder the conditions, the solution of the formula (3) can be obtained.
Obtaining the short-circuit current phasor modulus value of the formula (4) and obtaining the short-circuit current phasor modulus value through arrangement
The comparison curves of the two are shown in figure 3, the upper envelope curve of the dynamic phasor value curve ② is just the upper envelope curve of the instantaneous value curve ①, the lower envelope curve of the dynamic phasor value curve ② is just symmetrical to the lower envelope curve of the instantaneous value curve ① about a time axis, and the envelope curve of the instantaneous value curve ① can describe the attenuation law of the direct-current component of the short-circuit current and can also accurately give the amplitude of the alternating-current component.
The first peak of the curve ② is the inrush short-circuit current ipThe steady state value of the curve ② is the steady state short circuit current amplitudeThe lower envelope curve ① is obtained by symmetry of the lower envelope curve ② with respect to the time axis, and then averaged with the upper envelope curve ② to obtain the short-circuit current dc component idc(t), the initial value of the DC component corresponding to the fault time is A. The relationship between the initial value of the alternating current component of the short-circuit current and the initial value of the direct current component is
The method for obtaining the numerical solution of the instantaneous value curve ① is electromagnetic transient time domain simulation.
In the calculation of electromagnetic transient transients, surge short-circuit currents usually occur when the voltage crosses zero and a short-circuit occurs. For dynamic phasor simulation, the envelope shape of the dynamic phasor simulation is irrelevant to the fault occurrence time through module value calculation, so that the impulse short-circuit current can be always calculated.
Therefore, an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating-current system is established, and comprises the following steps: synchronous machine model, ac line model, transformer model, and reactive compensation and load model.
When a short circuit occurs in the near zone of the synchronous motor, the alternating current component of the short circuit current changes along with the change of the magnetic circuit of the motor, and generally attenuates along with the time. To describe this process, a dynamic phasor differential equation can be derived based on synchronous machine rotor, stator transient differential equations. If the change rule of the short-circuit current along with the excitation voltage needs to be further simulated, the action of an excitation system is further considered.
In engineering practice, a simplified model of the synchronous machine can generally be applied for short-circuit current calculation. On the one hand, the amount by which the alternating component of the short-circuit current is attenuated as the magnetic circuit of the machine changes is usually small in value. Only a very small fraction of the power supplies that provide short circuit current to the fault point belong to the "near end" generators. According to [1 ]]The given discrimination method needs to consider the attenuation of the alternating current component only when the high-voltage bus of the power plant is short-circuited. Thus, a fault occurring in the grid, for the most part, can be considered to be distantThe terminals are short-circuited. On the other hand, when the method is used for selecting the conductor and the electrical equipment, only the maximum short-circuit current needs to be concerned, so that the initial value I' of the alternating current component of the short-circuit current is consideredkSymmetrical on-off current IbSteady state short circuit current IkThe three are equal.
Under this allowable condition, the synchronous motor can be simulated as a sub-transient potential constant model. Using a constant voltage sourceInternal impedance ZS＝Ra+jX″dThe dynamic phasor differential equation of the synchronous motor is simulated and is expressed as an equation (6). Wherein the content of the first and second substances,is the generator terminal voltage.
For lumped parameter ac lines connected between nodes AB as shown in fig. 4. The dynamic phasor model expression is formula (7), formula (8) and formula (9).
For a longer line (e.g., greater than 300km), it may be equally divided into two or more segments, each segment using the model described above; or a dynamic phasor model applying the distribution parameters. Because the dynamic phasor of the three-phase symmetrical circuit still meets the positive, negative and zero sequence decoupling principle, for the zero sequence circuit of the circuit, only the above parameters need to be replaced by zero sequence parameters.
The single-phase equivalent circuit of the three-winding transformer related to the excitation branch is shown in figure 5, the influence of the excitation branch on the calculation of the short-circuit current is small and can be ignored, the nodes of the high, middle and low voltage sides respectively correspond to the 1, 2 and 3 end points in the figure, when the △ -shaped wiring winding forms a zero-sequence topology, the branch connected to the corresponding end point needs to be changed into the grounding, and for the double-winding transformer, only 1-N and 2-N branches need to be reserved.
The dynamic phasor equation is shown in formula (10) in FIG. 5.
in the formula：Zi＝Ri+jωLi，i＝1,2,3,m。
Formula (10) can be further abbreviated in the form of formula (11).
Both reactive compensation and load can be equivalent to a constant impedance, i.e. RL or RC series circuit, as shown in fig. 6. The dynamic phasor model expressions are formula (12) and formula (13).
And S102, converting the dynamic phasor model into an algebraic equation by using a trapezoidal integral method, and obtaining a conductance matrix of the fault node.
For the point-to-grid extra-high voltage half-wavelength transmission line shown in the attached figure 8, the element parameters are the same as those of the literature. The sending end power of the half-wavelength line is 5000MW in a steady state. The influence of measures (such as MOA) for suppressing overvoltage along the line is not considered in the simulation process. The current flowing through the circuit breaker on the J side of the half-wavelength line when three-phase short circuit occurs at different positions along the line is calculated by respectively using a dynamic phasor method (DP), an electromagnetic transient method (EMTP) and a GB/T15544 and 2013 standard simplification method (STD) provided by the text. During calculation, DP and EMTP both adopt line segment centralized parameters, and the length of each segment is 100 km. STD adopts line distribution parameter pi type equivalent model. The comparison of the A-phase current EMTP and the DP simulation curves at the positions of 300km and 2400km away from the J side during the fault are respectively shown in FIGS. 9 and 10. Extract I "from the curvek、ip、Ik、TdcThe short circuit current index was equal and compared to the STD method, as shown in table 1.
From the comparative analysis of fig. 9, fig. 10 and table 1, it can be seen that: (1) when a short circuit occurs at a location (300km) close to the power supply, the short circuit current has characteristics similar to fig. 3, i.e., the short circuit current includes two parts, i.e., an alternating current component and a direct current component, the amplitude of the alternating current component changes little during a fault period, and the direct current component gradually attenuates to zero. The results calculated by the EMTP, DP and STD methods have small deviation and are all within the engineering precision allowable range. (2) The short circuit current characteristics when the short circuit occurs for a location (2400km) far from the power supply are significantly different from fig. 3: the alternating current component of the short-circuit transformer is in a gradually increasing trend and can be transited to a short-circuit post-stable state after a period of time; the short circuit current contains almost no dc component, so the waveform has no significant bias. In this case, the short-circuit current peak ipNo longer occurs after the short circuit but occurs during the change of the alternating current component. The EMTP and DP calculation results have good consistency, but the STD method is not applicable any more. Because of this, GB/T15544-2013 mentions "special consideration is needed when the system nominal voltage is 500kV or above and contains a long-distance AC transmission line".
TABLE 1 comparison of short-circuit current results for different calculation methods
Waveform characteristics similar to the short circuit current of fig. 10 may also occur when a short circuit occurs near the series compensation capacitor in the power system. Short-circuit faults at these locations cause series resonance of the capacitor with the system inductive impedance, resulting in a significantly increased steady-state short-circuit current compared to other locations, and requiring a significant transient to reach this steady state. The standard simplified short-circuit current calculation method is not suitable for the situation, and the DP and EMTP methods have good adaptability.
The trapezoidal integration method is adopted in the text, and a damping coefficient α (0 is less than or equal to α is less than or equal to 1) is introduced to reduce the influence of numerical oscillation.
For the synchronous motor model, the trapezoidal integral formula is applied to the equation (6) in the time interval (t, t + delta t), and the form of the equation (14) is obtained through arrangement.
in the formula：
for the RL branch of the AC line, the formula (17) is obtained by applying the trapezoidal integral formula to the formula (7) and then arranging.
in the formula：
other components can also be transformed and derived to obtain a recursion form similar to the formula (14) and the formula (17), namely, the current flowing through the component at the moment t + delta t can be represented by the voltage applied to the component at the moment and a historical current source. The linear relationship of current and voltage is embodied as a calculated conductance, which is determined by the component parameters, system frequency and simulation step size. The historical current source is derived from the last time step variable and is therefore a known term for time t + Δ t.
The recursion formulas of all system elements are connected and written into a node conductance matrix according to the kirchhoff current law column in the form of
Namely, it is
The calculated voltage of each node at the t + delta t moment is used for updating and obtaining the current source item I (t + delta t) at the moment, so that the calculation is carried out
And step S103, performing triangular decomposition on the conductance matrix, and performing current calculation on the circuit with the fault by using a formula obtained after triangular decomposition.
The main flow of the program for calculating the short-circuit current by applying the dynamic phasor time domain simulation method is shown in fig. 7. It should be noted that the conductance matrix remains unchanged during the recursive calculation, so that only one time of formation and trigonometric decomposition is needed, and the calculation of the formula (21) only involves the previous generation and the next generation of the triangular matrix. Only when the network topology changes (such as setting a fault), the conductance matrix needs to be modified and decomposed again.
The conductance matrix has the same structure as the system admittance matrix, the dimension of the conductance matrix is equal to the number of system nodes, and the matrix is highly sparse. The optimized sequencing of the nodes is carried out, and the calculation efficiency can be greatly improved by applying the sparse storage and sparse vector technology.
When the dynamic phasor time domain simulation calculates the short-circuit current, only one specific fault can be performed each time the calculation process of fig. 7 is executed. When calculating the short-circuit currents of a plurality of nodes, it is necessary to perform the process a plurality of times.
When the asymmetric fault is calculated, a positive sequence network, a negative sequence network and a zero sequence network are required to be established like an electrical transient state, sequence conductance matrixes are respectively formed, and the three sequence conductance matrixes are coupled at the fault. Because the three-sequence network needs to perform time domain integration respectively, the fast calculation cannot be realized by the series-parallel connection of the complex sequence network impedance like the simplified calculation method of the short-circuit current.
The calculation result of the time domain simulation is a numerical curve, and comprises the short-circuit current of a fault point, the branch current flowing through a line or a transformer and the voltage of each node.
The short-circuit current obtained by the dynamic phasor time domain method is a numerical curve, as shown by a curve ② in FIG. 3. in engineering applications, the most practical numerical value includes the initial value I ″' of the alternating current component of the short-circuit currentkRush short-circuit current ipAnd the dc component of the short circuit current. Rush short-circuit current ipIt can be read directly from the short circuit current curve flowing through the fault point.
According to the calculation conditions in this document, the initial value I' of the AC component of the short-circuit current is generallykWith steady-state short-circuit current IkIdentical, therefore, I' can be taken directlyk＝Ik. In order to obtain steady-state short-circuit current IkThe simulation time should be guaranteed to be long enough. Generally, the attenuation time constant of the direct current component of the high-voltage transmission system is in the range of 45-120 ms, and can even reach more than 150ms at a node where a large-capacity generator or a large-capacity transformer is concentrated. The total duration of the dynamic phasor time domain simulation is 1s, and the accurate steady-state short-circuit current can be generally obtained.
As shown in FIG. 3, the curve of the DC component of the short-circuit current is the upper envelope line of the curve of the short-circuit current value minus the value Ik. The drawing of the envelope can be realized by a mathematical interpolation method.
The present application also provides a short-circuit current calculation apparatus 1100 based on the dynamic phasor time domain method, including:
the model establishing unit 1110 is configured to establish an element dynamic phasor model suitable for calculating a short-circuit current of a three-phase alternating-current system;
the conversion unit 1120 is configured to convert the dynamic phasor model into an algebraic equation by using a trapezoidal integration method, so as to obtain a conductance matrix of a fault node;
and a calculating unit 1130, configured to perform triangular decomposition on the conductance matrix, and perform current calculation on a circuit with a fault by using a formula obtained after the triangular decomposition.
Compared with the traditional simplified short-circuit current calculation method based on the element steady-state model, the method provided by the application can simulate the transient transition process of dynamic elements such as inductors and capacitors, and can calculate the full current curve including alternating current components and direct current components, so that the change condition of the short-circuit current along with time can be better described.
Compared with electromagnetic transient simulation, the method has small calculation amount, and can be conveniently initialized by the load flow calculation result, so that the method can be suitable for a large-scale power network without simplifying and equating the large-scale network like electromagnetic transient.
The method has good adaptability no matter in a conventional system or in an ultra-long line and a system containing series capacitance compensation, and can well envelope an electromagnetic transient simulation curve. And the key value of the short-circuit current required in the engineering can be quickly extracted through the dynamic phasor time domain simulation curve.
Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can make modifications and equivalents to the embodiments of the present invention without departing from the spirit and scope of the present invention, which is set forth in the claims of the present application.
Claims (4)
1. A short-circuit current calculation method based on a dynamic phasor time domain method is characterized by comprising the following steps:
establishing an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating-current system;
converting the dynamic phasor model into an algebraic equation by using a trapezoidal integral method to obtain a conductance matrix of a fault node;
and performing triangular decomposition on the conductance matrix, and performing current calculation on the circuit with the fault by using a formula obtained after triangular decomposition.
2. The method of claim 1, wherein the establishing a dynamic phasor model of the component suitable for use in the short circuit current calculation of the three-phase ac system comprises:
establishing a synchronous machine model, in particular, using a constant voltage sourceInternal impedance ZS＝Ra+jX”dThe dynamic phasor differential equation of the simulated synchronous motor is as follows. Wherein the content of the first and second substances,in order to be the generator terminal voltage,
the dynamic phasor model expression is as follows:
establishing an alternating current line model, wherein the dynamic phasor model expression is as follows:
the line can be equally divided into two or more sections, each section adopts the model, and the dynamic phasor of the three-phase symmetrical line still meets the positive, negative and zero sequence decoupling principle, so that for the zero sequence circuit of the line, the parameters are only replaced by zero sequence parameters;
establishing a transformer model, wherein the expression of a dynamic phasor model is as follows:
establishing a reactive compensation and load model, wherein the expression of a dynamic phasor model is as follows:
3. the method of claim 1, wherein the converting the dynamic phasor model into an algebraic equation using a trapezoidal integration method to obtain a conductance matrix of a fault node comprises:
a trapezoidal integral method is used, a damping coefficient is introduced, the dynamic phasor model is arranged to obtain a conductance matrix, the form is as follows,
4. a short-circuit current calculation device based on a dynamic phasor time domain method comprises the following steps:
the model establishing unit is used for establishing an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating-current system;
the conversion unit is used for converting the dynamic phasor model into an algebraic equation by using a trapezoidal integral method to obtain a conductance matrix of a fault node;
and the calculation unit is used for carrying out triangular decomposition on the conductance matrix and calculating the current of the circuit with the fault by using a formula obtained after the triangular decomposition.
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| CN112147396A (en) * | 2020-09-09 | 2020-12-29 | 中国电力科学研究院有限公司 | Method and system for calculating percentage of direct current component of short-circuit current |
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