CN110059346A - A kind of electro-magnetic transient rapid simulation method of controllable series compensator - Google Patents
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Abstract
The invention discloses a kind of electro-magnetic transient rapid simulation methods of controllable series compensator, include the following steps: step 1, get parms;The basic data of the system containing TCSC of acquisition, the inductance L including three-phase TCSC brancha、Lb、Lc, the capacitor C of three-phase TCSC brancha、Cb、Cc, three-phase current source iA、iB、iCExpression formula and initial trigger angle α0;Present invention introduces sinusoidal auxiliary variables, and the state equation of TCSC is converted into homogeneous linear differential equation group by linear nonhomogeneousState equation is unified in form under each operating condition, and the homogeneous linear differential equation group can pass through matrix exponetial integration method rapid solving;System model relative to required solution in traditional EM transient calculation can change in each time step, and in the present invention only when thyristor switching state changes, the system model of required solution can just change, therefore the present invention calculates more high efficiency and time conservation.
Description
Technical field
The present invention relates to electrical simulation technical fields, and in particular to a kind of electro-magnetic transient of controllable series compensator is quick
Emulation mode.
Background technique
Controllable series compensator (TCSC) is composed in parallel by the reactor that capacitor and thyristor control, brilliant by control
The Trigger Angle of brake tube changes topological structure, dynamically adjusts equivalent impedance, so that the series connection in extremely rapid succession controlling power transmission line is mended
Degree of repaying, improve the conveying capacity of transmission line of electricity, inhibit sub-synchronous oscillation etc..Along with power electronic devices performance promotion and make
The reduction of valence, TCSC is in electric system using more and more extensive.
Digital Simulation is to study one of the important means of power system dynamic step response, and can simulation model, which accurately reflect, is
The true dynamic behaviour of system will directly affect the confidence level and the thus correctness of prepared control strategy of simulation analysis result.
Currently, Digital Simulation is broadly divided into two major classes: electromechanical transient simulation and electromagnetic transient simulation.For electric power such as TCSC
Electronic component, electromechanical transient simulation have ignored equipment internal switch switching process, only consider operation of the equipment under positive sequence fundamental frequency
With control characteristic, influence, equipment internal control method for research unbalanced grid faults to equipment run bulk power grid
Influencing each other between short distance power electronic equipment after influencing, being disturbed, has significant limitation;Electromagnetic transient simulation is accurate
Circuit layer in face of equipment carry out three-phase modeling, in the form of instantaneous value present simulation result, being capable of accurate simulation power electronics
The fast transient process of equipment, but its calculating speed is very slow.
It is analyzed to seek a kind of not only suitable bulk power grid electromechanical transient process, but also can fully consider that power electronic equipment is quickly rung
The calculation method answered, electric system electromechanics-electromagnetic transient hybrid simulation technology are developed.Hybrid simulation sets power electronics
It is standby to be calculated using electromagnetic transient simulation;Then electromechanical transient simulation is used to simulate in external communication power grid.When more next
After more power electronic equipments penetrates into power grid, limited by electromagnetic transient simulation speed, the rapidity of hybrid simulation has been difficult to
Guarantee.Traditional electromagnetic transient simulation calculation method is improved just to seem very necessary.
Summary of the invention
The purpose of the present invention is to overcome the shortcomings of the existing technology and deficiency, provides a kind of electricity of controllable series compensator
Magnetic transient state rapid simulation method, this method can accurately reflect system is normal, under symmetrical and unbalanced fault TCSC dynamic row
To provide highly efficient timesaving method for the simulation of TCSC in electromechanics-electromagnetic transient hybrid simulation.
The purpose of the invention is achieved by the following technical solution:
A kind of electro-magnetic transient rapid simulation method of controllable series compensator, includes the following steps:
Step 1 gets parms;
The basic data of the system containing TCSC of acquisition, the inductance L including three-phase TCSC brancha、Lb、Lc, three-phase TCSC branch
Capacitor Ca、Cb、Cc, three-phase current source iA、iB、iCExpression formula and initial trigger angle α0;
Because the electric current in each phase line of TCSC is fundamental frequency sinusoidal quantity, without loss of generality, if its expression formula are as follows:
Meanwhile introducing sinusoidal auxiliary variable:
Step 2 asks initial time, i.e. the initial value X of t=0 moment state variable0;
If X0=[uca0 ila0 ucb0 ilb0 ucc0 ilc0 iA0 iB0 iC0 vA0 vB0 vC0]T, then:
When asking each phase capacitance voltage of TCSC and inductive current initial value, it need to be judged according to following formula (5) and (8)When, thyristor is on or off state;If conducting based on formula (6)
It calculates, is calculated if shutdown by formula (9), thereby determine that A, B, C phase initial capacitor voltage value uca0, ucb0, ucc0, A, B, C phase inductance electricity
Flow initial value ila0, ilb0, ilc0, so that it is determined that X0;
The conducting section of thyristor are as follows:
Inductive current and capacitance voltage expression formula are respectively as follows:
Wherein,
The shutdown section of thyristor are as follows:
Inductive current and capacitance voltage expression formula are respectively as follows:
Wherein,
V0=DLx(ωsinα+ω0Cos α tan λ β), (10)
Step 3 enables k=1;
Step 4, judges whether t is equal to 0;If so, going to step 10;If it is not, then going to step 5;
Step 5, t=t+ Δ t;
Step 6, judges whether thyristor switching situation changes;If so, going to step 7;If it is not, then going to
Step 11;
Judgment method is as follows: when having an on or off in any corresponding two thyristors in three-phase, being then considered as
Thyristor switching situation is changed;Wherein, turn on thyristors condition are as follows: effect has trigger pulse, and both ends on thyristor
Polarity of voltage is positive;Thyristor turns off time recognition method are as follows: as inductive current i under two neighboring Time steplxWhen contrary sign, i.e.,
ilx(t-Δt)×ilx(t) when < 0, or work as ilx(t- Δ t) ≠ 0 and ilx(t)=0 when, it is believed that when t moment is that thyristor turns off
It carves, and the inductive current i at the moment is setlx(t)=0, wherein x can use a, b, c;
Step 7 enables the finish time t of k-th of periodk ed=t;
Step 8, k=k+1;
Step 9, the initial time t of k-th of periodk st=t;
Step 10 forms three phase EOS;
If xa=[uca,ila]T, xb=[ucb,ilb]T, xc=[ucc,ilc]T, X=[xa xb xc iA iB iC vA vB vC]T,
The state equation of three-phaseSee below formula (11):
Wherein, AkxAnd BkxIndicate the matrix of k-th of period x phase, wherein x can use a, b, c phase;
When x phase have thyristor it is in the conductive state when:
When two thyristors of x phase are all in off state:
Step 11, solving state equation:
State equationSolution are as follows:
Step 12, judges whether t is greater than or equal to emulation end time tend;If so, terminating emulation;If it is not, then turning
To step 4.
The present invention have compared with prior art it is below the utility model has the advantages that
(1) present invention introduces sinusoidal auxiliary variables, and the state equation of TCSC is converted by linear nonhomogeneous
For homogeneous linear differential equation groupState equation is unified in form under each operating condition, and the linear homogeneous
Differential equation group can pass through matrix exponetial integration method rapid solving;
(2) system model relative to required solution in traditional EM transient calculation can change in each time step, this hair
In bright only when thyristor switching state changes, the system model of required solution can just change, therefore the present invention calculates more
Add high efficiency and time conservation.
Detailed description of the invention
Fig. 1 is flow chart of the invention;
Fig. 2 is the single system schematic diagram containing TCSC;
The inductive current and capacitance voltage waveform configuration schematic diagram of TCSC when Fig. 3 is stable state;
Fig. 4 is the present invention and PSCAD simulation result comparison schematic diagram under stable situation;
Fig. 5 is the present invention and PSCAD simulation result comparison schematic diagram when three-phase current source amplitude is symmetrically mutated;
Fig. 6 is the present invention and PSCAD simulation result comparison schematic diagram when single-phase current amplitude is mutated;
Fig. 7 is the present invention and PSCAD simulation result comparison schematic diagram when Trigger Angle is mutated;
Fig. 8 is the present invention and PSCAD simulation result comparison schematic diagram when C phase current source phase angle is mutated;
The present invention and PSCAD simulation result comparison schematic diagram when Fig. 9 is current source amplitude and phase angle simultaneous mutation.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Input of the present invention using three-phase fundamental frequency sinusoidal current as TCSC, adoption status space law arrange the state side for system of writing
Journey converts homogeneous linear differential equation group by linear nonhomogeneous for model by the processing of each step, this is neat
Sublinear Differential Equations group form when thyristor switching state changes can just change, thus be a kind of at times neat
Sublinear Differential Equations group, to improve calculating speed;The form for the homogeneous linear differential equation group established is as follows:
Wherein, X is the state variable of system;It is state matrix;K be period serial number (within a period,It keeps
It is constant);tk stIt is the initial time of k-th of period, corresponding state variable initial value is Xk st;tk edAt the end of being k-th of period
It carves, corresponding state variable end value is Xk ed.If t0=0 is emulation initial time, X0For t=t0The initial value of moment state variable,
There is following relationship to set up:
As shown in Fig. 2, describing solution throughway and solution procedure of the invention by taking the single system containing TCSC as an example.If imitative
The true period is t ∈ [0, tend], material calculation is Δ t (generally taking 50 μ s), and amount to be asked is the inductive current of three-phase TCSC branch
ila, ilb, ilcWith capacitance voltage uca, ucb, ucc;
As shown in Figure 1, a kind of electro-magnetic transient rapid simulation method of controllable series compensator, includes the following steps:
Step 1 gets parms;
The basic data of the system containing TCSC of acquisition, the inductance L including three-phase TCSC brancha、Lb、Lc, three-phase TCSC branch
Capacitor Ca、Cb、Cc, three-phase current source iA、iB、iCExpression formula and initial trigger angle α0;
As shown in figure 3, Trigger Angle is the electrical angle issued between the moment from capacitance voltage zero crossing to trigger pulse;
Because the electric current in each phase line of TCSC is fundamental frequency sinusoidal quantity, without loss of generality, if its expression formula are as follows:
Meanwhile introducing sinusoidal auxiliary variable:
In above-mentioned formula (1) and (2), I need to be obtainedAm、IBm、ICm,And ω;Obtaining above-mentioned numerical value is
The problem of research as needed, is arranged, i.e. the amount of these parameters is to solve for the amount that state variable must know.
Step 2 asks initial time, i.e. the initial value X of t=0 moment state variable0;
If X0=[uca0 ila0 ucb0 ilb0 ucc0 ilc0 iA0 iB0 iC0 vA0 vB0 vC0]T, then:
When asking each phase capacitance voltage of TCSC and inductive current initial value, it need to be judged according to following formula (5) and (8)When, thyristor is on or off state;If conducting based on formula (6)
It calculates, is calculated if shutdown by formula (9), thereby determine that A, B, C phase initial capacitor voltage value uca0, ucb0, ucc0, A, B, C phase inductance electricity
Flow initial value ila0, ilb0, ilc0, so that it is determined that X0;
The conducting section of thyristor are as follows:
Inductive current and capacitance voltage expression formula are respectively as follows:
Wherein,
The shutdown section of thyristor are as follows:
Inductive current and capacitance voltage expression formula are respectively as follows:
Wherein,
V0=DLx(ωsinα+ω0Cos α tan λ β), (10)
X in above-mentioned formula (6), (7), (9) and (10) can use a, b or c phase;
Step 3 enables k=1;
Step 4, judges whether t is equal to 0;If so, going to step 10;If it is not, then going to step 5;
Step 5, t=t+ Δ t;
Step 6, judges whether thyristor switching situation changes;If so, going to step 7;If it is not, then going to
Step 11;
Judgment method is as follows: when having an on or off in any corresponding two thyristors in three-phase, being then considered as
Thyristor switching situation is changed;Wherein, turn on thyristors condition are as follows: effect has trigger pulse, and both ends on thyristor
Polarity of voltage is positive;Thyristor turns off time recognition method are as follows: as inductive current i under two neighboring Time steplxWhen contrary sign, i.e.,
ilx(t-Δt)×ilx(t) when < 0, or work as ilx(t- Δ t) ≠ 0 and ilx(t)=0 when, it is believed that when t moment is that thyristor turns off
It carves, and the inductive current i at the moment is setlx(t)=0, wherein x can use a, b, c;
Step 7 enables the finish time t of k-th of periodk ed=t;
Step 8, k=k+1;
Step 9, the initial time t of k-th of periodk st=t;
Step 10 forms three phase EOS;
If xa=[uca,ila]T, xb=[ucb,ilb]T, xc=[ucc,ilc]T, X=[xa xb xc iA iB iC vA vB vC]T,
The state equation of three-phaseSee below formula (11):
Wherein, AkxAnd BkxIndicate the matrix of k-th of period x phase, wherein x can use a, b, c phase;
When x phase have thyristor it is in the conductive state when:
When two thyristors of x phase are all in off state:
Step 11, solving state equation:
State equationSolution are as follows:
Step 12, judges whether t is greater than or equal to emulation end time tend;If so, terminating emulation;If it is not, then turning
To step 4.
Following is a specific embodiment of the invention:
Using the power supply system of current source-TCSC shown in Fig. 2 as example.
In system, the current source for three-phase symmetrical is inputted:
Wherein,The π f=100 π of ω=2,TCSC's
Capacitor Ca=Cb=Cc=501.4 μ f, inductance La=Lb=Lc=2.01mH, initial trigger angle is α0=160 °;Amount to be asked is
The capacitance voltage and inductive current of three-phase.
(1) stable situation as shown in Figure 4;
(2) as shown in figure 5, when t=0.2s, ABC three-phase current source output current amplitude become original 1.2 times it is (right
Claim failure);
(3) as shown in fig. 6, when t=0.2s, A phase current source mutates, amplitude become initial value 0.6 times (it is asymmetric therefore
Barrier);
(4) as shown in fig. 7, when t=0.2s, Trigger Angle mutates, and becomes 170 ° (symmetric faults) from 160 °;
(5) as shown in figure 8, when t=0.2s, C phase current source phase angle mutates, Ic=ImSin (ω t+125 °) is not (right
Claim failure);
(6) as shown in figure 9, when t=0.2s, Trigger Angle mutates, and becomes 170 °, while C phase current source width from 160 °
Value mutation is 1.35 times (unbalanced faults) of open width value.
By Fig. 4~9 as it can be seen that acquired results of the present invention and electromagnetic transient simulation result are coincide well, institute of the present invention is demonstrated
State the validity of method.Meanwhile by following table 1 it is found that the present invention emulates time-consuming compared with electromagnetic transients program PSCAD
It is short, it has a clear superiority in calculating speed.
Compared with 1 present invention of table is time-consuming with PSCAD emulation
Present invention introduces sinusoidal auxiliary variables, and the state equation of TCSC is converted into together by linear nonhomogeneous
Sublinear Differential Equations groupState equation is unified in form under each operating condition, and the linear homogeneous differential
Equation group can pass through matrix exponetial integration method rapid solving;System mould relative to required solution in traditional EM transient calculation
Type can change in each time step, in the present invention only when thyristor switching state changes, the system model of required solution
Can just it change, therefore the present invention calculates more high efficiency and time conservation.
Above-mentioned is the preferable embodiment of the present invention, but embodiments of the present invention are not limited by the foregoing content,
His any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention, should be
The substitute mode of effect, is included within the scope of the present invention.
Claims (1)
1. a kind of electro-magnetic transient rapid simulation method of controllable series compensator, which is characterized in that include the following steps:
Step 1 gets parms;
The basic data of the system containing TCSC of acquisition, the inductance L including three-phase TCSC brancha、Lb、Lc, the capacitor of three-phase TCSC branch
Ca、Cb、Cc, three-phase current source iA、iB、iCExpression formula and initial trigger angle α0;
Because the electric current in each phase line of TCSC is fundamental frequency sinusoidal quantity, without loss of generality, if its expression formula are as follows:
Meanwhile introducing sinusoidal auxiliary variable:
Step 2 asks initial time, i.e. the initial value X of t=0 moment state variable0;
If X0=[uca0 ila0 ucb0 ilb0 ucc0 ilc0 iA0 iB0 iC0 vA0 vB0 vC0]T, then:
When asking each phase capacitance voltage of TCSC and inductive current initial value, it need to be judged according to following formula (5) and (8)When, thyristor is on or off state;If conducting based on formula (6)
It calculates, is calculated if shutdown by formula (9), thereby determine that A, B, C phase initial capacitor voltage value uca0, ucb0, ucc0, A, B, C phase inductance electricity
Flow initial value ila0, ilb0, ilc0, so that it is determined that X0;
The conducting section of thyristor are as follows:
Inductive current and capacitance voltage expression formula are respectively as follows:
Wherein,
The shutdown section of thyristor are as follows:
Inductive current and capacitance voltage expression formula are respectively as follows:
Wherein,
V0=DLx(ωsinα+ω0Cos α tan λ β), (10)
Step 3 enables k=1;
Step 4, judges whether t is equal to 0;If so, going to step 10;If it is not, then going to step 5;
Step 5, t=t+ Δ t;
Step 6, judges whether thyristor switching situation changes;If so, going to step 7;If it is not, then going to step
11;
Judgment method is as follows: when having an on or off in any corresponding two thyristors in three-phase, being then considered as brilliant lock
Pipe switching situation is changed;Wherein, turn on thyristors condition are as follows: effect has trigger pulse, and both end voltage on thyristor
Polarity is positive;Thyristor turns off time recognition method are as follows: as inductive current i under two neighboring Time steplxWhen contrary sign, i.e. ilx
(t-Δt)×ilx(t) when < 0, or work as ilx(t- Δ t) ≠ 0 and ilx(t)=0 when, it is believed that t moment is that thyristor turns off the moment,
And the inductive current i at the moment is setlx(t)=0, wherein x can use a, b, c;
Step 7 enables the finish time t of k-th of periodk ed=t;
Step 8, k=k+1;
Step 9, the initial time t of k-th of periodk st=t;
Step 10 forms three phase EOS;
If xa=[uca,ila]T, xb=[ucb,ilb]T, xc=[ucc,ilc]T, X=[xa xb xc iA iB iC vA vB vC]T, three
The state equation of phaseSee below formula (11):
Wherein, AkxAnd BkxIndicate the matrix of k-th of period x phase, wherein x can use a, b, c phase;
When x phase have thyristor it is in the conductive state when:
When two thyristors of x phase are all in off state:
Step 11, solving state equation:
State equationSolution are as follows:
Step 12, judges whether t is greater than or equal to emulation end time tend;If so, terminating emulation;If it is not, then going to step
Rapid four.
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CN117498284A (en) * | 2023-10-26 | 2024-02-02 | 武汉大学 | Series compensation capacitor device based on short-circuit fault current intelligent self-driving |
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