CN110083863B - Static reactive compensator-based electromagnetic transient rapid simulation method - Google Patents
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Abstract
The invention discloses an electromagnetic transient rapid simulation method based on a static var compensator, which comprises the following steps: acquiring basic parameters of an SVC device; the parameters to be acquired include: inductance L of TCR branch circuit, capacitance C of fixed capacitor FCsResistance R of filterfInductor LfAnd a capacitor CfExternal input voltage uA、uB、uCAnd a thyristor firing angle α; the method introduces a sine auxiliary variable, converts the state equation of the SVC from a non-homogeneous linear differential equation set into a homogeneous linear differential equation set, quickly obtains the solution of the equation set by a matrix exponential integration method, and meanwhile, the state equations under various working conditions are unified in form; compared with the traditional electromagnetic transient calculation in which the solution required system model changes at each time step, the method provided by the invention has the advantages that the solution required system model changes only when the on-off state of the thyristor changes, so that the calculation of the method provided by the invention is more efficient, and the working efficiency is greatly improved.
Description
Technical Field
The invention relates to the technical field of electrical simulation, in particular to an electromagnetic transient rapid simulation method based on a static var compensator.
Background
Static Var compensator svc (static Var compensator) is a power electronic device, and is usually composed of thyristor Controlled reactor tcr (thyristor Controlled reactor) and fixed capacitor fc (fixed capacitor). When the electric power system has a fault, the reactive power output by the SVC to the electric power system can be quickly and smoothly adjusted by quickly adjusting the trigger angle of the TCR in the SVC device, so that the purpose of adjusting the voltage of the electric power system is achieved. With the improvement of the performance of power electronic devices and the reduction of the manufacturing cost, the application of the SVC in power systems is more and more common.
Time domain simulation is an important means for researching the operating characteristics of the power system, and electromechanical transient simulation and electromagnetic transient simulation are two important contents of power system off-line simulation. For power electronic equipment, electromechanical transient simulation ignores the dynamic process inside the equipment, a quasi-steady-state modeling method is adopted, only the operation and control characteristics of the equipment under the positive sequence fundamental frequency are considered, and the method has great limitation on researching the influence of the asymmetric fault of the power grid on the equipment and the influence of the control method inside the equipment on the operation of a large power grid; the electromagnetic transient simulation carries out three-phase modeling on the power electronic equipment on an accurate circuit layer, has the advantages of accurate calculation, high reliability and the like, but has small calculation step length and low calculation speed.
In order to find a calculation method which is suitable for analyzing the electromechanical transient process of a large power grid and can fully consider the quick response of power electronic equipment, the electromechanical-electromagnetic transient hybrid simulation technology of a power system is developed. The hybrid simulation is used for performing electromagnetic transient simulation on the power electronic equipment by using a detailed device model, and performing electromechanical transient simulation on an external alternating current power grid, so that the rapid transient process of a specific device is reflected while the dynamic response of the large power grid is accurately obtained. When the infiltration level of power electronic equipment such as SVC is not high, the traditional hybrid simulation technology provides an effective means for researching the interaction between a large power grid and the power electronic equipment. With the scale enlargement of the power grid, more and more high-power electronic devices are connected into the power system. For the safety analysis of a large power grid, on the premise of ensuring the precision, it is necessary to develop a new method for electromagnetic transient modeling simulation of power electronic equipment such as SVC (static var compensator) with higher efficiency.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an electromagnetic transient rapid simulation method based on a static var compensator, which can accurately reflect the dynamic behavior of SVC under normal, symmetrical and asymmetrical states of a system, greatly improve the simulation speed while ensuring the calculation precision and greatly improve the working efficiency.
The purpose of the invention is realized by the following technical scheme:
an electromagnetic transient rapid simulation method based on a static var compensator comprises the following steps:
acquiring basic parameters of an SVC device; the parameters to be acquired include: inductance L of TCR branch circuit, capacitance C of fixed capacitor FCsResistance R of filterfInductor LfAnd a capacitor CfExternal input voltage uA、uB、uCAnd a thyristor firing angle α;
because the phase voltages input into each phase line of the SVC are fundamental frequency sinusoidal quantities, and the generality is not lost, an expression of three-phase fundamental wave components of the connection bus voltage is shown as the following formula (1):
and introducing auxiliary variables as shown in the following formula (2):
step two, finding the initial value X of the state variable at the initial time, namely, at the time when t is 00:
X0=[i1(0),i2(0),i3(0),uaf(0),iaf(0),ubf(0),ibf(0),ucf(0),icf(0),uA(0),uB(0),uC(0),vA(0),vB(0),vC(0)]T,
Wherein:
step three, making k equal to 1;
step four, judging whether t is equal to 0 or not; if yes, turning to the step ten; if not, turning to the fifth step;
step five, t is t + [ delta ] t;
judging whether the on-off condition of the thyristor changes or not; if yes, go to step seven; if not, go to step eleven;
the method for judging the on-off condition of the thyristor specifically comprises the following steps: when one of the two thyristors corresponding to any one of the three branches of the TCR is switched on or off, the on-off state of the thyristor is considered to be changed; wherein, the conduction condition of the thyristor is as follows: when the thyristor acts with trigger pulse, and the polarity of the voltage at the two ends is positive; the turn-off conditions of the thyristor were: when two adjacent calculation time steps are different in sign of the inductive current, namely: i.e. ix(t-Δt)·ix(t) < 0, or when ix(t- Δ t) ≠ 0 and ixWhen (t) is 0, the thyristor is considered to be turned off at the time t, and the inductive current i at the time is juxtaposedx(t)=0;
Step eight, k is k + 1;
Wherein:
wherein, the matrix Z, F, W is a constant matrix, which is respectively:
wherein, the matrix LkThe matrix is changed along with the period and is formed according to the on-off condition of the TCR branch thyristor in the kth period;
Lk=[LAB,LBC,LCA]T,
the three-phase TCR branch circuit thyristor on-off conditions comprise:
when the thyristor between the AB phases is in a conducting state, LAB=[1/L -1/L 0]When both thyristors between the AB phases are in the OFF state, LAB=[0 0 0];
When a thyristor is in a conducting state between BC phases, LBC=[0 1/L -1/L]When both thyristors between the BC phases are in the OFF state, LBC=[0 0 0];
When a thyristor is in a conducting state between the CA phases, LCA=[-1/L 0 1/L]When both thyristors between CA phases are in OFF state, LCA=[0 0 0];
Step twelve, absorbing three-phase current Y ═ i by SVCa,ib,ic]TCan be determined by Y ═ BX, where matrix B is:
step thirteen, judging whether t is larger than tend(ii) a If yes, ending the program; if not, returning to the fourth step.
Compared with the prior art, the invention has the following beneficial effects:
(1) the method introduces a sine auxiliary variable, converts the state equation of the SVC from a non-homogeneous linear differential equation set into a homogeneous linear differential equation set, quickly obtains the solution of the equation set by a matrix exponential integration method, and meanwhile, the state equations under various working conditions are unified in form;
(2) compared with the traditional electromagnetic transient calculation in which the solution required system model changes at each time step, the method provided by the invention has the advantages that the solution required system model changes only when the on-off state of the thyristor changes, so that the calculation of the method provided by the invention is more efficient, and the working efficiency is greatly improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic three-phase connection diagram of a six-pulse TCR-FC type SVC device according to the present invention;
FIG. 3 is a schematic view of the firing angle α of the present invention;
FIG. 4 is a schematic diagram showing comparison of simulation results under symmetrical steady-state operation of the present invention;
FIG. 5 is a schematic diagram showing a comparison of simulation results when a three-phase power supply amplitude sudden change occurs in the present invention;
FIG. 6 is a diagram showing comparison of simulation results when the amplitude of the A-phase power supply suddenly changes according to the present invention;
FIG. 7 is a schematic diagram showing a comparison of simulation results under the condition of sudden change of the firing angle during symmetrical steady-state operation;
FIG. 8 is a diagram showing a comparison of simulation results when the amplitude of the A-phase power supply and the flip angle are suddenly changed at the same time.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
The invention takes three-phase fundamental frequency sinusoidal voltage as input of SVC, adopts a state equation of a state space method column writing system, converts a model from a non-homogeneous linear differential equation set into a homogeneous linear differential equation set through processing of each step, and the form of the homogeneous linear differential equation set can be changed when the on-off state of a thyristor is changed, so that the homogeneous linear differential equation set is divided into time intervals and can be solved through a matrix exponential integration method, thereby improving the calculation speed.
The form of the established homogeneous system of linear differential equations is as follows:
wherein X is a state variable of the system;is a state matrix; k is a time period number; t is tk stIs the starting time of the kth time interval, and the initial value of the corresponding state variable is Xk st;tk edIs the end time of the kth time interval, and the corresponding state variable has the end value of Xk ed. The following relationship holds:
the solving idea and solving steps of the present invention are described as shown in the six-pulse TCR-FC type SVC device of FIG. 2. In FIG. 2, uaf、iaf、ubf、ibf、ucf、icfAnd the capacitance voltage and the inductance current of each phase of the filter branch circuit are represented.Let the simulation time period be t e [0, t ∈end]The calculation step is delta t (generally 50 mu s), and the three-phase input voltage u of the system is calculatedA、uB、uCThe inductance current i of the TCR branch is a known quantity1、i2、i3And SVC absorbed three-phase current ia、ib、icIs the amount to be requested.
As shown in fig. 1, a method for rapidly simulating an electromagnetic transient based on a static var compensator includes the following steps:
acquiring basic parameters of an SVC device; the parameters to be acquired include: inductance L of TCR branch circuit, capacitance C of fixed capacitor FCsResistance R of filterfInductor LfAnd a capacitor CfExternal input voltage uA、uB、uCAnd a thyristor firing angle α;
as shown in fig. 3, the firing angle α is the electrical angle from the TCR leg inductance voltage zero crossing to the time the firing pulse is emitted.
Because the phase voltages input into each phase line of the SVC are fundamental frequency sinusoidal quantities, and the generality is not lost, an expression of three-phase fundamental wave components of the connection bus voltage is shown as the following formula (1):
and introducing auxiliary variables as shown in the following formula (2):
in the above formulas (1) and (2), U is acquiredAm、UBm、UCm,And ω. Wherein, UAm、UBm、UCmAndrespectively externally input three-phase voltage uA、uB、uCThe amplitude and phase angle of (d); ω is related to the frequency f of the system, ω 2 π f.
Step two, obtaining an initial value X of the state variable at the initial time, namely, the time when t is equal to 00:
X0=[i1(0),i2(0),i3(0),uaf(0),iaf(0),ubf(0),ibf(0),ucf(0),icf(0),uA(0),uB(0),uC(0),vA(0),vB(0),vC(0)]T,
Wherein:
step three, making k equal to 1;
step four, judging whether t is equal to 0 or not; if yes, turning to the step ten; if not, turning to the fifth step;
step five, t is t + [ delta ] t;
judging whether the on-off condition of the thyristor changes or not; if yes, go to step seven; if not, turning to the eleventh step;
the method for judging the on-off condition of the thyristor specifically comprises the following steps: when one of the two thyristors corresponding to any one of the three branches of the TCR is switched on or off, the on-off state of the thyristor is changed; wherein, the conduction condition of the thyristor is as follows: when the thyristor acts with trigger pulse, and the polarity of the voltage at the two ends is positive; the turn-off conditions of the thyristor were: when two adjacent calculation time steps are different in sign of the inductive current, namely: i all right anglex(t-Δt)·ix(t) < 0, or when ix(t- Δ t) ≠ 0 and ixWhen (t) is 0, the thyristor is considered to be turned off at the time t, and the inductive current i at the time is juxtaposedx(t) ═ 0; wherein, x can be 1, 2 or 3; i.e. ix(t) represents the current in any of the TCR legs.
Step eight, k is k + 1;
Wherein:
wherein, the matrix Z, F, W is a constant matrix, which is respectively:
wherein, the matrix LkThe matrix is changed along with the period and is formed according to the on-off condition of the TCR branch thyristor in the kth period;
Lk=[LAB,LBC,LCA]T,
the three-phase TCR branch circuit thyristor on-off conditions comprise:
when the thyristor between the AB phases is in a conducting state, LAB=[1/L -1/L 0]When both thyristors between the AB phases are in the OFF state, LAB=[0 0 0];
When a thyristor is in a conducting state between BC phases, LBC=[0 1/L -1/L]When both thyristors between the BC phases are in the OFF state, LBC=[0 0 0];
When a thyristor is in a conducting state between the CA phases, LCA=[-1/L 0 1/L]When both thyristors between CA phases are in OFF state, LCA=[0 0 0];
Step twelve, absorbing three-phase current Y ═ i by SVCa,ib,ic]TCan be determined by Y ═ BX, where matrix B is:
step thirteen, judging whether t is larger than tend(ii) a If yes, ending the program; if not, returning to the fourth step.
The following is a specific embodiment of the present invention:
taking the six-pulse TCR-FC type SVC device shown in fig. 2 as an example, the calculation result is compared with the calculation result of the present invention by using PSCAD/EMTDC electromagnetic transient simulation software. In the system, three-phase symmetrical voltage sources are input:
wherein U isAm=UBm=Ucm10kV, w 2 pi f 100 pi, inductance L0.0975H of TCR branch, filteringResistance R of the device branchf0.1 Ω, inductance Lf10H, capacitance CfThe capacitance C of the capacitor FC is fixed at 200 μ Fs3 μ F, flip angle α 100 °; the simulation calculation step length is 50 mus, and the simulation duration is 1 s.
(1) The system runs symmetrically and stably;
the simulation results are as follows: FIG. 4(a) shows the current i of the TCR branch1、i2、i3(b) gives the three-phase current i absorbed by the SVC from the systema、ib、icThe waveform of (a); the black dotted line is the calculation result of PSCAD/EMTDC electromagnetic transient software, and the black solid line is the calculation result of the invention.
(2) The system generates a three-phase voltage drop fault with the duration of 0.06s at a power supply end of 0.1s, and the voltage amplitude falls from 10kV to 7 kV;
the simulation results are as follows: FIG. 5(a) shows the current i of the TCR branch1、i2、i3(b) gives the three-phase current i absorbed by the SVC from the systema、ib、icThe waveform of (a); the black dotted line is the calculation result of PSCAD/EMTDC electromagnetic transient software, the black solid line is the calculation result of the invention, and the black dotted line is the time when the fault occurs.
(3) The system has an A-phase voltage dropping fault with the duration of 0.06s at a power supply end of 0.1s, and the voltage amplitude drops from 10kV to 7 kV;
the simulation results are as follows: FIG. 6(a) shows the current i of the TCR branch1、i2、i3(b) gives the three-phase current i absorbed by the SVC from the systema、ib、icThe waveform of (a); the black dotted line is the calculation result of PSCAD/EMTDC electromagnetic transient software, the black solid line is the calculation result of the invention, and the black dotted line is the time when the fault occurs.
(4) When the system operates symmetrically and stably, the triggering angle alpha is mutated at 0.1s and is changed from 100 degrees to 115 degrees;
the simulation results are as follows: FIG. 7(a) shows the current i for the TCR branch1、i2、i3(b) gives the three-phase current i absorbed by the SVC from the systema、ib、icThe waveform of (a); the black dotted line is the calculation result of PSCAD/EMTDC electromagnetic transient software, the black solid line is the calculation result of the invention, and the black dotted line is the moment of sudden change of the trigger angle.
(5) The system has an A-phase voltage drop fault with the duration of 0.06s at a power supply end of 0.1s, the voltage amplitude is dropped from 10kV to 7kV, and the trigger angle alpha is changed from 100 degrees to 115 degrees;
the simulation results are as follows: FIG. 8(a) shows the current i of the TCR branch1、i2、i3(b) gives the three-phase current i absorbed by the SVC from the systema、ib、icThe waveform of (a); the black dotted line is the calculation result of PSCAD/EMTDC electromagnetic transient software, the black solid line is the calculation result of the invention, and the black dotted line is the time when the fault occurs.
As can be seen from FIGS. 4 to 8, the result obtained by the method is well matched with the electromagnetic transient simulation result, and the effectiveness of the method is verified. Meanwhile, as can be seen from the following table 1, compared with the electromagnetic transient simulation program PSCAD, the simulation of the present invention is short in time consumption and has an obvious advantage in calculation speed.
TABLE 1 comparison of the invention with PSCAD simulation elapsed time
The invention introduces a sine auxiliary variable, converts the state equation of the SVC from a non-homogeneous linear differential equation set into a homogeneous linear differential equation set, quickly obtains the solution of the equation set by a matrix exponential integration method, and simultaneously, the state equations under various working conditions are unified in form; compared with the traditional electromagnetic transient calculation in which the solution required system model changes at each time step, the method provided by the invention has the advantages that the solution required system model changes only when the on-off state of the thyristor changes, so that the calculation of the method provided by the invention is more efficient, and the working efficiency is greatly improved.
The present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents and equivalents thereof, which are intended to be included in the scope of the present invention.
Claims (1)
1. An electromagnetic transient rapid simulation method based on a static var compensator is characterized by comprising the following steps:
acquiring basic parameters of an SVC device; the parameters to be acquired include: inductance L of TCR branch circuit, capacitance C of fixed capacitor FCsResistance R of filterfInductor LfAnd a capacitor CfExternal input voltage uA、uB、uCAnd a thyristor firing angle α;
because the phase voltages input into each phase line of the SVC are fundamental frequency sinusoidal quantities, and the generality is not lost, an expression of three-phase fundamental wave components of the connection bus voltage is shown as the following formula (1):
wherein t represents time, UAm、UBm、UCmRespectively A, B, C phase voltage amplitudes, initial phase angle, v, of A, B, C phase voltageA、vB、vCA, B, C auxiliary variables, respectively;
and introducing auxiliary variables as shown in the following formula (2):
step two, solving the initial value X of the state variable at the moment when t is equal to 00:
X0=[i1(0),i2(0),i3(0),uaf(0),iaf(0),ubf(0),ibf(0),ucf(0),icf(0),uA(0),uB(0),uC(0),vA(0),vB(0),vC(0)]T,
Wherein:
step three, making k equal to 1, wherein k represents a time interval serial number;
step four, judging whether t is equal to 0 or not; if yes, turning to the step ten; if not, turning to the fifth step;
step five, t is t + [ delta ] t;
step six, judging whether the on-off condition of the thyristor changes; if yes, go to step seven; if not, turning to the eleventh step;
the method for judging the on-off condition of the thyristor specifically comprises the following steps: when one of the two thyristors corresponding to any one of the three branches of the TCR is switched on or off, the on-off state of the thyristor is considered to be changed; wherein, the conduction condition of the thyristor is as follows: when a trigger pulse acts on the thyristor, the polarity of the voltage at two ends is positive; when one of the following two conditions is met, the thyristor is turned off at the moment t, and the inductive current i at the moment is juxtaposedx(t)=0:
Two adjacent calculation time steps have different signs of the inductive current, and the formula is as follows: i.e. ix(t-Δt)·ix(t)<0;
② the inductive current in two adjacent calculation time steps conforms to ix(t- Δ t) ≠ 0 and ix(t)=0。
Step eight, k is k + 1;
Wherein:
Lka matrix representing a random transformation;
wherein, the matrix Z, F, W is a constant matrix, which is respectively:
wherein, the matrix LkThe matrix is changed along with the period and is formed according to the on-off condition of the TCR branch thyristor in the kth period;
Lk=[LAB,LBC,LCA]T,
the three-phase TCR branch circuit thyristor on-off conditions comprise:
when the thyristor between the AB phases is in a conducting state, LAB=[1/L -1/L 0]When both thyristors between the AB phases are in the OFF state, LAB=[0 0 0];
When a thyristor is in a conducting state between BC phases, LBC=[0 1/L -1/L]When both thyristors between the BC phases are in the OFF state, LBC=[0 0 0];
When a thyristor is in a conducting state between the CA phases, LCA=[-1/L 0 1/L]When both thyristors between CA phases are in OFF state, LCA=[0 0 0];
Step twelve, absorbing three-phase current Y ═ i by SVCa,ib,ic]TCan be determined by Y ═ BX, where matrix B is:
step thirteen, judging whether t is larger than tend(ii) a If yes, ending the program; if not, returning to the fourth step.
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