CN109635374B - Short-circuit current calculation method and device based on dynamic phasor time domain method - Google Patents
Short-circuit current calculation method and device based on dynamic phasor time domain method Download PDFInfo
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Abstract
The application discloses 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 the fault node; and carrying out triangular decomposition on the conductance matrix, and carrying out current calculation on a circuit with faults by using a formula obtained after the triangular decomposition, thereby solving the problem of insufficient calculation accuracy of a short circuit current standard simplified practical calculation method under the condition of short circuit of a remote power transmission line, a serial compensation capacitor and the like.
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 simultaneously relates to a short-circuit current calculation device based on the dynamic phasor time domain method.
Background
Short-circuit current calculation is the conventional content of power system analysis, and short-circuit current calculation needs to be carried out for electrical equipment selection, conductor set relay protection setting values and the like. Short-circuit process simulation in a power system relates to electromagnetic transient calculation, but the application of the existing electromagnetic transient calculation method for calculating short-circuit current is difficult due to the huge scale of an actual power system. The aim of the calculation standardization of the short-circuit current is to obtain the maximum or minimum short-circuit current of the system by a simplified practical method, and the equipment safety and the investment saving are taken into consideration. At present, various standards at home and abroad adopt a simplified method to calculate short-circuit current, and the requirements of engineering calculation can be generally met.
The short-circuit current calculation method includes short-circuit current alternating-current component initial value, direct-current component decay time constant, impulse 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 the algebraic solving problem of the power frequency steady-state circuit, and the calculation process of the short-circuit current is greatly simplified. However, the short-circuit current alternating-current component calculation result obtained by the method is essentially a steady-state solution of the short-circuit current power frequency component. 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 series compensation or ultra-long high-voltage alternating current lines, the fault current when the elements are short-circuited presents an obvious transition process, the steady state of the alternating current component can be reached after several or even more than ten cycles, and the practical short-circuit current calculation method is not applicable any more. Therefore, the problem of insufficient calculation accuracy of the short-circuit current standard simplified practical calculation method under the condition that short-circuit occurs in the vicinity of a remote transmission line and a series compensation capacitor and the like exists in the prior art.
Disclosure of Invention
The application provides a short circuit current calculation method based on a dynamic phasor time domain method, which solves the problem of insufficient calculation precision of a short circuit current standard simplified practical calculation method under the condition that short circuits occur in the vicinity of a remote transmission line and 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 the fault node;
and performing triangular decomposition on the conductance matrix, and performing current calculation on a circuit with faults by using a formula obtained after the triangular decomposition.
Preferably, the building an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating current system comprises the following steps:
establishing a synchronous motor model, particularly by using a constant voltage sourceInternal impedance Z S ＝R a +jX″ d The dynamic phasor differential equation of the analog synchronous motor is as follows. Wherein (1)>For the generator terminal voltage to be the same,
the expression of the dynamic phasor model is as follows:
establishing an alternating current circuit model, wherein the expression of the dynamic phasor model is as follows:
the circuit can be equally divided into two sections or multiple sections, each section adopts the model, and as the dynamic phasors of the three-phase symmetrical circuit still meet the principle of positive, negative and zero sequence decoupling, the zero sequence circuit of the circuit only needs to replace the parameters with zero sequence parameters;
establishing a transformer model, wherein the expression of the dynamic phasor model is as follows:
and (3) building a reactive compensation and load model, wherein the expression of the dynamic phasor model is as follows:
preferably, the step of converting the dynamic phasor model into an algebraic equation by using a trapezoidal integral method to obtain a conductance matrix of the fault node includes:
a trapezoidal integral method is used, damping coefficient is introduced, a dynamic phasor model is arranged, a conductance matrix is obtained, the form is as follows,
the application also provides a short-circuit current calculating device based on a dynamic phasor time domain method, which comprises the following components:
the model building unit is used for building 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 the fault node;
and the calculation unit is used for carrying out triangular decomposition on the conductance matrix and carrying out current calculation on the circuit with faults 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, and the curve of the dynamic phasor model time domain simulation can be enveloped by the electromagnetic transient simulation curve, so that 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 in a long-distance transmission line, near a series compensation capacitor and the like is solved.
Drawings
Fig. 1 is a schematic diagram of a method for calculating a short-circuit current 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 through a resistive high-speed short circuit according to an embodiment of the present application;
FIG. 3 is a schematic diagram showing the relationship between the curves of formula (2) and formula (5) according to the embodiment of the present application;
FIG. 4 is a centralized parameter circuit model in accordance with an embodiment of the present application;
FIG. 5 is a three-winding transformer model that accounts for the excitation branches 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 schematic diagram of a process flow of 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-network extra-high voltage half-wavelength ac transmission model according to an embodiment of the present application;
fig. 9 is a graph showing current at a three-phase short circuit at a 300KM position according to an embodiment of the present application;
fig. 10 is a graph showing current at a 24KM position three-phase short circuit according to an embodiment of the present application;
fig. 11 is a schematic diagram of a short-circuit current calculating device 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. The present application may be embodied in many other forms than those herein described, and those skilled in the art will readily appreciate that the present application may be similarly embodied without departing from the spirit or essential characteristics thereof, and therefore the present application is not limited to the specific embodiments disclosed below.
Referring to fig. 1, fig. 1 is a schematic diagram of 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 provided by the embodiment of the present application is described in detail below with reference to fig. 1.
Step S101, an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating current system is established.
Before an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating current system is established, the short-circuit current curve is analyzed first.
For the circuit shown in fig. 2, the constant alternating voltage source u with the angular velocity omega is controlled by a resistor R and an inductor L at t 0 Time=0 short-circuited, the instantaneous value equation is equation (1), where p is the differential operator.
The short-circuit current analysis 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) comprises two parts, namely 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 direct current component is zero.
Converting formula (1) into a dynamic phasor equation
Wherein the power supply voltageFor a constant phasor, a solution of formula (3) can be found by applying a Lawster transform and taking into account the edge condition.
Taking the short-circuit current phasor module value of (4), and finishing to obtain
The expressions (2) and (5) are short-circuit current expressions when the voltage source is short-circuited by RL. The difference is that the former is an instantaneous value time domain solution and the latter is a dynamic phasor time domain solution. The comparison curves are shown in figure 3, and 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 of the dynamic phasor value curve (2) is exactly symmetrical to the lower envelope of the instantaneous value curve (1) about the time axis. The envelope curve of the instantaneous value curve (1) can describe the attenuation rule of the direct current component of the short-circuit current, and the amplitude of the alternating current component can be accurately given. Based on this feature, dynamic phasor time domain simulation can be applied to short circuit current calculation of large-scale power grids.
The first peak of curve (2), i.e. the rush short-circuit current i p The method comprises the steps of carrying out a first treatment on the surface of the The steady state value of the curve (2) is the steady state short circuit current amplitudeFrom the lower package of curve (2)The line is symmetrical about the time axis to obtain the lower envelope of the curve (1), and then the lower envelope of the curve (2) is averaged to obtain the short-circuit current DC component i dc (t) the initial value of the direct current component corresponding to the time of failure is a. The relation between the initial value of the alternating current component and the initial value of the direct current component of the short-circuit current is +.>
For general networks, it is very difficult to obtain an analytical solution of the short-circuit current curve, and a time-domain integration method is generally applied in engineering to obtain a numerical solution of the short-circuit current curve. The method for obtaining the numerical solution of the instantaneous value curve (1) is electromagnetic transient time domain simulation. For a large-scale power network, the problems of large calculated amount, long calculated time, difficult initialization and the like are faced to the full electromagnetic transient simulation. The dynamic phasor time domain simulation can better solve the problems, and the calculation amount can be greatly reduced because the dynamic phasor time domain simulation is essentially the time domain simulation of the phasor; and by applying the load flow calculation result, the dynamic phasor simulation initialization can be conveniently carried out.
In the calculation of electromagnetic transient instantaneous values, an impulse short-circuit current generally occurs when a short circuit occurs at the moment of zero crossing of the voltage. In the dynamic phasor simulation, the envelope curve shape is irrelevant to the occurrence time of the fault after the module value calculation, so that the impact short-circuit current can be always calculated.
Thus, building an element dynamic phasor model suitable for short-circuit current calculation of a three-phase alternating current system comprises: synchronous motor model, ac line model, transformer model, reactive compensation and load model.
When short circuit occurs in the near region 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, the alternating current component is attenuated with time. To describe this process, the dynamic phasor differential equation of the synchronous machine rotor, stator transient differential equation can be derived based thereon. If the change rule of the short-circuit current along with the exciting voltage needs to be further simulated, the action of the exciting system should be further considered.
In engineering practice, it is generally applicableAnd (5) calculating short-circuit current by using a simplified model of the synchronous motor. On the one hand, the amount by which the short-circuit current ac component decays as the motor magnetic circuit changes is generally small in value. Of the power supplies that provide short-circuit current to the fault point, only a very small fraction belongs to the "near-end" generator. According to [1 ]]The given discrimination method only needs to consider the attenuation of the alternating current component of the high-voltage bus of the power plant when the high-voltage bus is short-circuited. Thus, faults occurring in the grid can for the most part be considered as far end shorts. On the other hand, when the method is used for selecting conductors and electrical equipment, only the maximum short-circuit current is concerned, so that the initial value I' of the alternating current component of the short-circuit current is considered k Symmetrically breaking current I b Steady state short circuit current I k The three are equal.
Under this permissible condition, the synchronous motor can be modeled as a sub-transient potential constant model. By a constant voltage sourceInternal impedance Z S ＝R a +jX″ d The dynamic phasor differential equation of the analog synchronous motor is shown as formula (6). Wherein (1)>Is the generator terminal voltage.
For a concentrated parametric ac line connected between nodes AB, as shown in fig. 4. The dynamic phasor model expression is expressed by the formulas (7), (8) and (9).
For longer lines (such as more than 300 km), the line can be divided into two or more sections, and each section adopts the model; or a dynamic phasor model of the distribution parameters is applied. Because the dynamic phasors of the three-phase symmetrical circuit still meet the principle of positive, negative and zero sequence decoupling, the zero sequence circuit of the circuit only needs to replace the parameters with zero sequence parameters.
The single-phase equivalent circuit of the three-winding transformer related to the excitation branch is shown in fig. 5, and the influence of the excitation branch on the calculation of the short-circuit current is small and can be ignored. The nodes at the high, medium and low voltage sides respectively correspond to the endpoints 1, 2 and 3 in the attached drawings. For delta-wired windings, when forming their zero sequence topology, the branches connected to the respective endpoints need to be changed to ground. For a double winding transformer, only two branches of 1-N and 2-N are reserved.
The dynamic phasor equation is shown in figure 5 as equation (10).
in the formula ：Zi ＝R i +jωL i ，i＝1,2,3,m。
Formula (10) may be further abbreviated as the form of formula (11).
Both reactive compensation and load can be equivalently constant impedance, i.e., RL or RC series circuits, as shown in fig. 6. The dynamic phasor model expression is expressed by the formulas (12) and (13).
And S102, converting the dynamic phasor model into an algebraic equation by using a trapezoidal integral method to obtain a conductance matrix of the fault node.
For the point-to-network ultra-high voltage half-wavelength transmission line shown in fig. 8, the element parameters are the same as those in the literature. And the half-wavelength line transmitting end power is 5000MW in a steady state. The effect of measures (e.g., MOA) to suppress line overvoltage is not considered during the simulation. And calculating the current flowing through the circuit J side breaker when three-phase short circuits occur at different positions along the half-wavelength circuit by using a dynamic phasor method (DP), an electromagnetic transient method (EMTP) and a GB/T15544-2013 standard simplified method (STD) respectively. During calculation, DP and EMTP adopt line segment centralized parameters, and each segment is 100km long. STD adopts a line distribution parameter pi-type equivalent model. The comparison of the simulation curves of the phase A current EMTP and the DP at the fault positions of 300km and 2400km at the J side is shown in the accompanying figures 9 and 10 respectively. Extracting I' from the curve k 、i p 、I k 、T dc The short-circuit current index was equal and compared with the STD method as shown in Table 1.
From the comparative analysis of fig. 9, 10 and table 1, it can be seen that: (1) When a short circuit occurs at a position (300 km) closer to the power supply, the characteristics of the short circuit current are similar to those of fig. 3, namely, the short circuit current comprises an alternating current component and a direct current component, the amplitude of the alternating current component changes little during the fault period, and the direct current component gradually decays to zero. The deviation of the results obtained by calculation of the EMTP, DP and STD methods is not large and is within the allowable range of engineering precision. (2) When a short circuit occurs at a position (2400 km) far from the power supply, the characteristics of the short circuit current are significantly different from those of fig. 3: the alternating current component of the power supply is gradually increased, and the power supply can be transited to a steady state after short circuit after a period of time; the short-circuit current contains almost no direct current component, so the waveform has no obvious bias. In this case, the short-circuit current peak i p The short-circuit is no longer present in the latter half cycle, but rather in the course of the change of the alternating current component. The EMTP and DP calculation results have good consistency, but the STD method will not be applicable. As such, it is proposed in GB/T15544-2013Special consideration is required to the point that when the system is rated at 500kV and above and contains long-distance ac transmission lines.
Table 1 comparison of short-circuit current results for different calculation methods
A waveform characteristic 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 inductive impedance of the system, thus having a significantly increased steady state short circuit current compared to other locations, and requiring significant transients to reach the steady state. The standard simplified short-circuit current calculation method is not applicable to the situation, and the DP and EMTP methods have good adaptability.
By applying the trapezoidal integral method, a dynamic phasor model expressed by a differential equation can be converted into an algebraic equation. A trapezoidal integration method is adopted, and a damping coefficient alpha (alpha is more than or equal to 0 and less than or equal to 1) is introduced, so that the influence of numerical oscillation is reduced.
For the synchronous motor model, the equation (6) is applied to a trapezoidal integral equation over a time interval (t, t+Δt), and the equation (14) is obtained through finishing.
in the formula ：
for the RL branch of the ac line, the equation (7) is applied to the trapezoidal integral equation, and the equation (17) is obtained by sorting.
in the formula ：
other elements can also be transformed and deduced to obtain a recursive form of the formulae (14) and (17), i.e. the current flowing through the element at time t+Δt can be represented by the voltage applied to the element at that time and a historical current source. The linear relationship between current and voltage is embodied in calculated conductance, which is determined by the element parameters, system frequency and simulation step size. The history current source is derived from the variable of the previous time step and is therefore known for the time t + at.
The recursive formulas of all the system elements are combined and written as a node conductance matrix according to the kirchhoff current law column as follows
I.e.
The calculated voltage of each node at the time t+delta t is applied to update and obtain a current source item I (t+delta t) at the time, thereby calculating
And step S103, performing triangular decomposition on the conductance matrix, and performing current calculation on the circuit with faults by using a formula obtained after the triangular decomposition.
The main flow of the process for calculating the short-circuit current by using 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 computation, so that the computation of equation (21) only involves the generation of the triangular matrix and the generation of the recurrence. Only when a network topology change (e.g., a set fault) occurs, the conductance matrix needs to be modified and re-decomposed.
The structure of the conductance matrix is the same as that of 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 ordering 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 short-circuit current is calculated by the dynamic phasor time domain simulation, the calculation process of fig. 7 can be performed only for one specific fault at a time. When calculating the short-circuit currents of a plurality of nodes, it is necessary to perform this process a plurality of times.
When calculating an asymmetric fault, it is necessary to build up a positive, negative, zero three-order network like an electromechanical transient, and form an order conductance matrix respectively, the three-order conductance matrices being coupled at the fault. Because the three-sequence network needs to respectively perform time domain integration, rapid calculation can not be realized through series-parallel connection of the impedance of the complex-sequence network like the simplified calculation method of the short-circuit current.
The calculation result of the time domain simulation is a numerical curve, including the short circuit current of the fault point, the branch current flowing through the line or the 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 values include: initial value I' of short-circuit current alternating current component k Impact short-circuit current i p And a dc component of the short circuit current. Impact short-circuit current i p Can be read directly from the short-circuit current curve flowing through the fault point.
According to the calculation conditions herein, the initial value I' of the alternating current component of the short-circuit current is generally k And steady state short circuit current I k The same applies to the direct taking of I k ＝I k . To obtain steady-state short-circuit current I k The simulation time should be guaranteed to be long enough. In general, the decay time constant of the dc component in the high-voltage power transmission system ranges from 45 ms to 120ms, and can reach 150ms or more at the node where the high-capacity generator or the high-capacity transformer is concentrated. The total duration of the dynamic phasor time domain simulation is 1s, and accurate steady-state short-circuit current can be obtained generally.
As can be seen from fig. 3, the dc component curve of the short-circuit current is the upper envelope of the short-circuit current value curve minus the value I k . The drawing of the envelope can be achieved by mathematical interpolation.
The application also provides a short-circuit current calculating device 1100 based on a dynamic phasor time domain method, which comprises:
a model building unit 1110, configured to build an element dynamic phasor model suitable for calculating a short-circuit current of a three-phase ac 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 the fault node;
and a calculating unit 1130, configured to perform trigonometric decomposition on the conductance matrix, and perform current calculation on the circuit that has failed using a formula obtained after the trigonometric 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 process of dynamic elements such as inductance, capacitance and the like, and can calculate the full-current curve containing alternating current components and direct current components, so that the condition of the change of the short-circuit current along with time can be better described.
Compared with electromagnetic transient simulation, the method has small calculated amount, and can be conveniently initialized by the tide calculation result, so that the method is applicable to a large-scale power network, and the method does not need to simplify and equate the large-scale network like electromagnetic transient.
The method has good adaptability in both conventional systems and ultra-long lines and systems with series capacitance compensation, and can well envelope electromagnetic transient simulation curves. The key value of the short-circuit current required in the engineering can be rapidly extracted through the dynamic phasor time domain simulation curve.
The above embodiments are only for illustrating the technical solution of the present application and not for limiting the same, and although the present application has been described in detail with reference to the above embodiments, one skilled in the art may make modifications and equivalents to the specific embodiments of the present application, and any modifications and equivalents thereof without departing from the spirit and scope of the present application are within the scope of the claims of the present application.
Claims (3)
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 short-circuit current of a three-phase alternating current system, comprising the following steps:
establishing a synchronous motor model, particularly by using a constant voltage sourceInternal impedance Z S ＝R a +jX″ d The dynamic phasor differential equation of the analog synchronous motor is as follows, wherein +.>For the generator terminal voltage to be the same,
the expression of the dynamic phasor model is as follows:
wherein ,for generator sub-transient potential +.>Is the generator terminal voltage, R is a resistor, L d "is the sub-transient inductance,the current vector is a generator current vector, j is an imaginary symbol, and ω is a power frequency angular velocity;
establishing an alternating current circuit model, wherein the expression of the dynamic phasor model is as follows:
wherein ,for node A voltage, +.>For node A current, +.>For node B current, L is reactance, +.>The current of the line is C, C is a capacitor, and p is a differential operator;
the circuit can be equally divided into two sections or multiple sections, each section adopts the model, and as the dynamic phasors of the three-phase symmetrical circuit still meet the principle of positive, negative and zero sequence decoupling, the zero sequence circuit of the circuit only needs to replace the parameters with zero sequence parameters;
establishing a transformer model, wherein the expression of the dynamic phasor model is as follows:
wherein ,the node voltage matrix at the time t is taken as a node voltage matrix, and Z is taken as an impedance matrix;
and (3) building a reactive compensation and load model, wherein the expression of the dynamic phasor model is as follows:
wherein ,for node 1 voltage, +.>For node 2 voltage, +.>For node C voltage, ">For the node 1 current to be present,current for node 2;
converting the dynamic phasor model into an algebraic equation by using a trapezoidal integral method to obtain a conductance matrix of the fault node;
and performing triangular decomposition on the conductance matrix, and performing current calculation on a circuit with faults by using a formula obtained after the triangular decomposition.
2. The method of claim 1, wherein said converting the dynamic phasor model into an algebraic equation using a trapezoidal integration method to obtain the conductance matrix of the failed node comprises:
a trapezoidal integral method is used, damping coefficient is introduced, a dynamic phasor model is arranged, a conductance matrix is obtained, the form is as follows,
wherein G is the electric conductivity,for the node voltage matrix at time t+Δt, I (t) is the current at time t.
3. A short circuit current calculation device based on a dynamic phasor time domain method, comprising:
the model building unit is used for building an element dynamic phasor model suitable for calculating the short-circuit current of the three-phase alternating current system, and comprises the following components:
establishing a synchronous motor model, particularly by using a constant voltage sourceInternal impedance Z S ＝R a +jX″ d The dynamic phasor differential equation of the analog synchronous motor is as follows, wherein +.>For the generator terminal voltage to be the same,
the expression of the dynamic phasor model is as follows:
wherein ,for generator sub-transient potential +.>Is the generator terminal voltage, R is a resistor, L d "is the sub-transient inductance,is the generator current vector;
establishing an alternating current circuit model, wherein the expression of the dynamic phasor model is as follows:
wherein ,for node A voltage, +.>For node A current, +.>For node B current, L is reactance, +.>The line current and C is a capacitor;
the circuit can be equally divided into two sections or multiple sections, each section adopts the model, and as the dynamic phasors of the three-phase symmetrical circuit still meet the principle of positive, negative and zero sequence decoupling, the zero sequence circuit of the circuit only needs to replace the parameters with zero sequence parameters;
establishing a transformer model, wherein the expression of the dynamic phasor model is as follows:
wherein ,the node voltage matrix at the time t;
and (3) building a reactive compensation and load model, wherein the expression of the dynamic phasor model is as follows:
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 the fault node;
and the calculation unit is used for carrying out triangular decomposition on the conductance matrix and carrying out current calculation on the circuit with faults by using a formula obtained after the triangular decomposition.
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