CN106446428A - Switching circuit electromagnetic transient analysis method and device - Google Patents
Switching circuit electromagnetic transient analysis method and device Download PDFInfo
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Abstract
The invention provides a switching circuit electromagnetic transient analysis method and device. The analysis method includes the steps of establishing a state equation of a circuit, modifying the state equation of circuit topology which changes at the moment of switching motion, reinitializing the potentials of all nodes of the circuit after the switching motion, solving the state equation of the circuit, and conducting switching circuit transient analysis according to calculated state quantities at all moments. The analysis device comprises an equation establishment module, an adjustment module, an initialization module, a switching circuit solving module and a switching transient analysis module. According to the technical scheme, the long-standing problem that it is difficult to compile a state equation of a common circuit network is solved, and the state equation method can be applied to electromagnetic transient analysis of the large-scale circuit network; besides, the method for compiling the state equation is simple, short in calculation time and very suitable for being implemented in computer programming.
Description
Technical field
The present invention relates to power system circuit electro-magnetic transient numerical simulation field, in particular to a kind of on-off circuit electromagnetism
Transient analysis method and analytical equipment.
Background technology
The normal destruction run of power system is caused by short circuit mostly, and such as big short circuit current makes element rupture, electricity
The poly- fall of pressure causes system cracking even to collapse, to electromagnetic interference of electrical equipment etc..When being short-circuited, system is from a kind of state
Become another kind of state, and with the complicated Transient Electromagnetic Phenomena of generation.
Modal analysis and state Equation Method are included to Electromagnetic Transient Analysis of Power System method.
General EMTP at present, the software such as PSCAD/EMTDC, real-time simulator RTDS and electromagnetic transient in power system divide
Analysis software is used mostly the modal analysis of doctor's H.W.Dommel proposition in 1969 as rudimentary algorithm.Modal analysis is first
Selected integration method and time step, by equivalent with dynamic elements such as electric capacity for inductance become promise pause current source, specific at each
Circuit equivalent is resistor network by the moment, is solved by building the conductance matrix of circuit.The major defect of modal analysis
It is selected integration method and time step can not change, otherwise circuit will be modeled again, seriously reduce simulation efficiency；With
When, modal analysis, in the electromagnetic transient problems proposition that power system development is for AC system in early days, is not especially closed
Switching characteristic in note circuit, when perfect switch action, modal analysis needs column circuits equation again, and this also can reduce imitative
True efficiency.
State Equation Method be first build circuit network system model dynamical equation, and then select suitable integration method and
Time step solving, and modal analysis ratio, state Equation Method has very big flexibility.Legacy Status equation method main not
It is in place of foot to be typically not directly available the state equation of circuit, need the capacitance voltage in selection circuit and inductive current conduct
The quantity of state of circuit, for increasingly complex medium scale circuit network it is necessary to knowledge by network graph theory, by complexity
Topological analysis obtain.The state equation of circuit network is compiled excessively complicated, especially when containing controlled source in circuit, often
It is difficult to form required canonical form.On the other hand, after circuit occurs perfect switch action, circuit topology changes
Become, need again to write the state equation of circuit.
Preconditioning technique is usually used in software at present, the state equation of topologys all in circuit is saved in internal memory,
Switching circuit equation during switch motion.And when there is a large amount of perfect switch in circuit, calculating and preserving all possible topology
Equation will be the unaffordable computation burden of computer.At present, the software of use state equation method have Matlab,
SimPowerSystem, PLECS etc., real-time simulator RT-LAB solves in module in its on-off circuit and also using state equation
Method.
For meeting the needs of prior art development, improve speed and the efficiency of circuit analysis, it is desirable to provide a kind of transient state electricity
Road analysis method and analytical equipment, it is ensured that analyze speed and efficiency, reduce amount of calculation.
Content of the invention
For meeting the needs of prior art development, realize the emulation to on-off circuit for the computer programming, the invention provides
A kind of on-off circuit electromagnetic transient analysis method for computer software design.
The on-off circuit electromagnetic transient analysis method that the present invention provides, it thes improvement is that, described analysis method includes：
S1, according to switch circuit topology build circuit state equation；
S2, receive switch motion information after, change the state equation of circuit topology changing；
S3, receive switch motion information after, reinitialize each node potential of circuit；
The state equation of the circuit of modification after S4, solution switch motion；
S5：On-off circuit transient analysis is carried out according to the quantity of state in calculated each moment.
Further, in described step S1, the structure of state equation includes：
(1-1) digitization of circuit topology：Node to circuit network and branch number select ground reference node；
(1-2) determine coefficient matrix：
Define n+1 rank neutral element square formation KR、KLAnd KC, and n+1 rank neutral element vector Is；
Branch road execution false code circulation, and coefficient square formation and vectorial depression of order are processed as n rank；
(1-3) coefficient matrix and Circuits System equation is used to build the circuit state equation shown in following formula (1)：
Further, described false code circulation includes：
(1.1) it is calculated as follows resistance branch：
(1.2) then it is calculated as follows inductive branch：
(1.3) it is calculated as follows capacitive branch：
(1.4) it is calculated as follows voltage source branch road and the positive pole of voltage source is connected with node j：
(1.5) it is calculated as follows current source branch and the forward direction of current source points to node j's by node i：
Wherein, Rs：Ideal voltage source internal resistance value；R：The resistance value of resistance branch；L：The inductance value of inductive branch；C：Electric capacity
The capacitance of branch road；Us：The output voltage values of ideal voltage source branch；Is：The output current value of current source branch.
Further, shown in described Circuits System equation such as following formula (2)：
In formula,It is n rank column vector,The current potential of corresponding node n；KR、KLAnd KC：It is respectively
N level matrix number；Is：N rank power supply column vector；
Coefficient matrix K1、K2, R and x as follows：
E is unit diagonal matrix；
Further, shown as the following formula coefficient matrix changes t in described step S20State side after moment switch motion
Journey：
Wherein, KrIt is the equivalent conductance matrix of switching branches, remove WithOutward, KrIn other elements other be zero；KR,+：Resistance coefficient matrix before switch motion；
KR,-：Resistance coefficient matrix after switch motion.
Further, the heavy initialization operation described in step S3 is shown below：
Wherein,Node potential is in time
Integration amount；Is,d+：The Norton equivalent electric current source information of ideal voltage source；Δt0=td+-td-：The minimum time
Step-length；xd+And xd-：Represent t respectivelyd+And td-The quantity of state in moment.
Further, in step S4 circuit the Iteration Recursive Solution shown in state equation following formula：
Wherein, Δ t is the time step between moment n and moment n+1；β is an alternative coefficient；RnIt is the moment
Input vector corresponding to n, Rn+1It is the input vector corresponding to the n+1 moment.
Further, described alternative factor beta can value include：β=0, is front to Euler method；β=0.5, for ladder
Shape method；Or, β=1, for backward Euler method.
Further, the quantity of state according to each moment calculating obtains simulation curve, carries out on-off circuit transient analysis.
A kind of on-off circuit electromagnetic transient analysis device, described analytical equipment includes：Establishing equation module, adjusting module,
Initialization module, on-off circuit solve module and switching transients analysis module；
Described establishing equation module builds state equation according to circuit topology figure, and receiving circuit switch motion information；
Described adjusting module adjusts state equation after described establishing equation module receives contactor action message
Coefficient matrix；
Described initialization module initializes node potential, and according to the capacitance voltage in circuit and inductive current to node electricity
Position carries out weight initialization operation；
Described on-off circuit solves module immediate integration Recursive Solution state equation；
Described switching transients analysis module carries out on-off circuit transient analysis according to the quantity of state in calculated each moment.
Further, described establishing equation module includes digitization module, loop module and matrix generation module；
Circuit topology information is stored in a computer by described digitization module with digitization form；
Described loop module includes resistance branch, inductive branch, capacitive branch, voltage source branch road and current source branch circulation
The false code calculating；
Described matrix generation module eliminates the 0th row and the 0th row of each coefficient matrix, generates n rank square formation.
Further, the function of described digitization module includes：
(1) node serial number to circuit network, and select ground reference node；
(2) branch number to circuit, and stored in a computer with the form sequentially forming digitization of branch number；
(3) build the system equation of circuit topology.
Further, comprise the corresponding pass of coefficient matrix between state equation and system equation in described matrix generation module
System, is shown below：
Wherein, E is unit diagonal matrix.
Moreover with immediate prior art ratio, the present invention provide technical scheme there is following excellent effect：
1. the technical scheme that the present invention provides, after digitization circuit topology, determines coefficient matrix combined circuit system side
Journey builds on-off circuit state equation, solves the difficult problem that general circuit network for a long time compiles state equation, makes state side
Application in large-scale circuit network electromagnetic transient analysis for the journey method is possibly realized, and the present invention provide compile state equation
Method is succinct, processes every branch road successively, with little need for the time of calculating, is very suitable for computer programming and realizes.
2nd, the technical scheme that the present invention provides after in the switch motion moment, circuit topology changes it is only necessary to according to switch
State is modified to the several elements in equation coefficient matrix, you can modification state equation is it is not necessary to row write state side again
Journey, significantly improves the simulation efficiency of on-off circuit.
3rd, the technical scheme that the present invention provides in the switch motion moment, enter to circuit by the backward Euler method using minimum step-length
Row weight initialization operation, is easy to computer programming and realizes, simulation process neatly changes integration method and time step.
Brief description
The on-off circuit electromagnetic transient analysis method flow diagram that Fig. 1 provides for the present invention；
Fig. 2 is the closure/off-state schematic diagram of perfect switch branch road；
Fig. 3 is the schematic equivalent circuit of switch motion moment electric capacity；
Fig. 4 is the schematic equivalent circuit of switch motion moment inductance；
Fig. 5 is that in embodiment, supply frequency is the circuit topology schematic diagram of 50Hz；
Fig. 6 is simulation result comparison diagram in embodiment.
Specific embodiment
Below with reference to the detailed technical scheme introducing present invention offer in the way of specific embodiment of Figure of description.
The present invention proposes a kind of linear switching circuit electromagnetic transient analysis method, with node potential and node potential with
The integration amount of time is state variable, according to the annexation of branch road, the quick voltage obtaining branch road and electric current, processing procedure letter
Single；Using the node potential of circuit as quantity of state, set up state equation, and discrete time iterative carried out to state equation,
Obtain the transient state accordingly result of circuit；In the switch motion moment, circuit equation is modified and behaviour is initialized to circuit again
Make, to ensure transient response continuity in time.
The technical scheme that the present invention provides mainly includes：
First, set up the state equation of circuit, and solving state equation；
(1) digitization of circuit topology；
The node of circuit network is numbered, and selectes ground reference node；To the branch number in network, and with
The form sequentially forming digitization of branch number, as shown in table 1 below branch road information table：
Table 1 branch road information table
(2) obtain coefficient matrix；
Step 1:Define n+1 rank neutral element square formation KR, KLAnd Kc, and n+1 rank neutral element vector Is, in matrix and vector
Element numbers be 0～n；
Step 2：To the execution pseudo-code below circulation of all of branch road：
For Each Branch
If branch road is resistance branch：
If branch road is inductive branch：
If branch road is capacitive branch：
If branch road is voltage source branch road, and the positive pole of voltage source is connected with j node：
If branch road is current source branch, and the positive direction of current source points to j node by i node：
End For
Step 3：Eliminate square formation KR, KLAnd KCIn the 0th row and the 0th row, become three n rank square formations；Eliminate vectorial IsIn
No. 0 element, become n rank column vector.
Wherein：RsRepresent the internal resistance value of ideal voltage source, take a minimum real constant here, in general sense circuit
The 10 of minimum resistance-8To 10-6Times；R represents the resistance value of resistance branch, and L represents the inductance value of inductive branch, and C represents electric capacity
The capacitance of branch road；Us is the output voltage values of ideal voltage source branch；Is is the output current value of current source branch.
(3) use the system equation of coefficient matrix combined circuit, form state equation：
The system equation of circuit is shown below：
Wherein,It is n rank column vector, each element value represents the current potential of corresponding node.
The rule of correspondence in the middle of state equation and system equation is：
Wherein, E is unit diagonal matrix.
State equation is formed according to the matrix being formed in step (2) and the rule of correspondence (2), is shown below：
(4) carry out Recursive Solution with immediate integration, obtain numerical value on each time point for state variable x.Directly amass
The Iteration of point-score is shown below：
Wherein, Δ t is the time step between moment n and moment n+1；β is an alternative coefficient, when β area not
With value when, related names are as shown in table 2 below：
The selection of table 2 β and numerical stability
| β | Title | Stability | Numerical precision |
| 0 | Forward direction Euler method | Conditional stability | Single order precision |
| 0.5 | Trapezoidal method | Unconditional stability | Second order accuracy |
| 1 | Backward Euler method | Unconditional stability | Single order precision |
Wherein, trapezoidal method has the numerical precision of second order, is unconditional stability simultaneously, quilt in the analysis of linear problem
Widely used.
2nd, when the switch motion in circuit, the topology of circuit can change, in switch motion time adjustment circuit shape
State equation；
First, the perfect switch in circuit to be considered as a kind of basic bypass elements, as being connected to No. i and j
For bypass elements between number node, there are closed and disconnected two states as shown in Figure 2 in perfect switch：
A, when switch is in closure state, the current potential of i-node and j node is equal, is equivalent to the voltage source of a 0V even
It is connected between two nodes, its equivalent circuit is the current source of one 0A of resistor coupled in parallel of the ohm that goes to zero；
B, when switch is off, contact between two nodes is cut off it is not necessary to carry out any constraint.
Therefore, if the switch being connected between two nodes of i, j is in t0Moment generation action, then in t0Repair before and after moment
Resistance coefficient matrix K in change-based (1)R, quickly can change coefficient matrix using the method shown in formula (5) it is not necessary to right
Original circuit equation is decomposed and is regenerated, can the effectively save calculating time：
Wherein, KrIt is the equivalent conductance matrix of switching branches, remove WithOutward, KrIn other elements other be zero；KR,+：Resistance coefficient matrix before switch motion；
KR,-：Resistance coefficient matrix after switch motion.
3rd, after switch motion, the heavy initialization operation of circuit.
When switch motion causes circuit topology in tdWhen moment changes, node potential therein is possible in tdMoment
There is saltus step in front and back, the numerical oscillation of interdependent node current potential when calculating using trapezoidal method, can be caused.This is accomplished by switching time
To circuit, each node potential carries out reinitializing operation.
(1) classical initialization operation
According to Circuit theory, before and after switch motion, capacitive branch has the characteristic keeping two ends potential difference constant, and inductance props up
There is the characteristic keeping branch current constant on road, therefore can be in tdIn the moment, electric capacity is equivalent to electricity according to method as described in Figure 2
Potential source, inductance is equivalent to current source according to method as shown in Figure 3, according to td-The capacitance voltage in moment and inductive current calculate
td+The Potential distribution in moment.
If all having done the dynamic elements such as the electric capacity in circuit, inductance after equivalent process, in circuit, only exist resistance branch
And current source branch, still can obtain static circuit equation (6) according to the false code trying to achieve coefficient matrix, be shown below：
In solution formula (6)Initialization after switch motion for the circuit can be completed.
At this moment, except comprising information K of resistance branch and voltage source internal resistance branch road in coefficient matrix KR,d+Outward, further comprises
Internal resistance information K of capacitor equivalent voltage sourceRC, it is shown below：
K=KR,d++KRC, wherein KRC=∑CKrc(7)
For some is connected between node i and node j, electric capacity is the branch road of C, KrcIn contain its equivalent one-tenth desired electrical
After potential source, with regard to its internal resistance Rs(RsGo to zero) branch road information.Matrix KrcIn remove
WithIn addition, other elements are zero.
Norton equivalent electric current source information I comprising all current sources and ideal voltage source in primary circuit is removed in vectorial Is,d+
In addition, further comprises information I of inductance equivalent current sourceL,d-And information I of capacitor equivalent ideal voltage sourcesc,-, such as following formula
(8) shown in：
I=Is,d++IL,d-+ISC,d-(8)
Wherein, IL,d-=∑LIl,d-,ISC,d-=∑cIsc,d-.Some is connected between node i and node j, inductance
For measuring as the branch road of L, IlIn contain the information of its equivalent current source.Except Il,d-(i)=IL,d-And Il,d-(j)=IL,d-Outward,
Vectorial Il,d-In other elements be zero.It is connected between node i and node j simultaneously for some, capacitance is propping up of C
For road, IscIn contain its equivalent promise and pause electric current source information.Vectorial Isc,d-In, except Isc,d-(i)=Isc,d-And Isc,d-(j)=
Isc,d-Outward, other elements are zero.
(7) and (8) are substituted into (6), and is organized into the form as shown in following formula (9)：
Wherein, L_relate=IL, d-；
(2) the backward Euler method weight initialization operation of switching time；
If in switch motion moment td, with a minimum time step Δ t0(Δt0=td+-td-) to state equation
(3) apply backward Euler method, using td-The quantity of state x in momentd-, try to achieve td+The quantity of state x in momentd+, computation scheme such as formula (10)
Shown：
Wherein,WithUnder
Footmark d- and d+ represent respectively switch motion complete before and after the completion of time instant.
Formula (10) is further spread out as formula (11) and (12).
In view of Δ t0The fact that tend to 0, formula (12) is deformed into formula (13), shows that node potential integration amount in time exists
Do not change before and after switch motion.
Ψd+=Ψd-(13)
Formula (13) is updated to formula (11), and arranges the form of an accepted way of doing sth (14), be shown below：
If formula (14) and formula (9) are of equal value, illustrate in the switch motion moment, once the rear difference operation of little step-length is true
On complete an opportunity classical theory node potential weight initialization operation.
(3) formula (14) and the equivalence of formula (9) are proved, including proving the equivalence of inductance continuous item and electric capacity continuous item
Equivalence；
(3-1) equivalence proof of inductance continuous item：
For inductive branch shown in for Fig. 4 a, following formula is set up：
Il,d-=L-1[Ψd-(i)-Ψd-(j)] (15)
Or write as matrix format, be shown below：
Continue to expand to：
Because each inductive branch has formula (17) to set up, the therefore inductance continuous item I in formula (9)L,d-=∑LIl,d-
With the inductance continuous item K in formula (14)Lψd-=∑LKlΨd-It is of equal value.
(3-2) equivalence of electric capacity continuous item
Consider the Norton equivalent current source of the capacitive branch shown in Fig. 3 c, the electric capacity continuous item in formula (9) can expand into
Formula (18) and formula (19)：
By electric capacity continuous item in formula (14)According to each capacitive branch write as expansion form for example formula (20) and
Shown in formula (21)：
By the electric capacity correlation in formula (14)Write as expansion form such as formula according to each capacitive branch
(22) and shown in formula (23)：
Due toRepresent td-Magnitude of voltage on moment electric capacity, simultaneously takes account of RSWith Δ t0
The fact that all go to zero, electric capacity continuous item in formula (9)With the electric capacity continuous item in formula (14)
Of equal value.
Above content demonstrated in the switch motion moment, was equivalent to according in circuit to Euler method using after minimum step-length
Capacitance voltage and inductive current heavy initialized operation to node potential, with other EMTP using modal analysis, EMTDC etc.
Software is compared, and simulation process neatly changes integration method and time step.
A kind of on-off circuit electromagnetic transient analysis device includes：Establishing equation module, adjusting module, initialization module, open
Close circuit and solve module and switching transients analysis module；
Establishing equation module sets up state equation according to circuit topology figure, and receiving circuit switch motion information；
Establishing equation module includes digitization module, loop module and matrix generation module；
Circuit topology information is stored in a computer by digitization module with digitization form；The work(of digitization module
Can include：
(1) node serial number to circuit network, and select ground reference node；
(2) branch number to circuit, and stored in a computer with the form sequentially forming digitization of branch number；
(3) build the system equation of circuit topology.
Loop module includes resistance branch, inductive branch, capacitive branch, voltage source branch road and current source branch cycle calculations
False code；
Matrix generation module eliminates the 0th row and the 0th row of each coefficient matrix, generates n rank square formation；Eliminate vectorIn No. 0
Element, becomes n rank column vector.
Include the rule of correspondence between state equation and system equation in matrix generation module, be shown below：
Wherein, E is unit diagonal matrix.
Adjusting module adjusts the coefficient matrix of state equation after establishing equation module receives contactor action message；
Initialization module initialization node potential simultaneously enters to node potential according to the capacitance voltage in circuit and inductive current
Row weight initialization operation；
On-off circuit solves module and carries out Recursive Solution state equation with immediate integration；
Switching transients analysis module carries out on-off circuit transient analysis according to the quantity of state in calculated each moment.
Embodiment
A bridge-type current source rectification circuit as shown in Figure 5, digitization module is by the circuit topology information of Fig. 5 with table 3
Form in the computer that circuit topology is stored by shown form, carries out emulation point using the technical scheme that the present invention provides
Analysis, basic step size settings are 2ms.
The branch road information of table 3 example
First 1～No. 5 branch road in table 3 is executed with the false code of storage in loop module, and is obtained by matrix generation module
To coefficient matrix such as formula (25)～(28).
Thus obtaining system equation (29) and the state equation (30) of circuit.
WhereinE is unit diagonal matrix.
The quantity of state defining zero moment is x0=(0,0,0,0,900,0,0,0,0,0)T.
Front half period, in the 0+ moment, due to the one-way conduction characteristic of ideal diode, D2 and D3 will open, D1 simultaneously
It is held off with D4.With reference to the rule of formula (5), adjusting module is by the resistance coefficient matrix K of original stateRIt is revised as KR1, as formula
(31).
KR1=KR+KD2+KD3(31)
Wherein
When difference calculating after single step is carried out by on-off circuit solution module, because D2 and D3 is open-minded in zero moment, in order to avoid
Numerical oscillation occurs, this is to need to apply a backward-difference method, to obtain the quantity of state in 0+ moment.This backward difference computing
Time step take Δ t0=10-7S, and by Δ t0Substitute into formula (4) with β=1, obtain t=10-7The system state amount in s momentAs formula (32).
Wherein
Carry out trapezoidal iterative calculation, subsequent adjustment time step-length is Δ t=0.002-10-7S, according to t=10-7The s moment
System state amountObtain quantity of state x during t=2ms using formula (33)0.002.Again step-length is adjusted to Δ t=0.002s,
Calculate system state amount when 4ms, 6ms, 8ms and 10ms using formula (33) successively.
In second half of the cycle, in the t=10ms moment, D2 and D3 turns off, D1 and D4 turns on, with reference to the rule of formula (5), will be front
The coefficient matrix K of half period21It is revised as the K of second half of the cycle22, as formula (34) and (35).
KR2=KR1-KD2-KD3+KD1+KD4(35)
Wherein
As front half period, in the t=10ms moment of circuit topology switching, take Δ t0=10-7S, obtains t=0.01
+10-7The system state amount in s momentAfter then passing through the adjustment of a step-length, step-length is fixed as 2ms, calculates successively
Obtain system state amount when 12ms, 14ms, 16ms, 18ms and 20ms.
Switching transients analysis module, to analysis of simulation result, emulates the inductive drop obtaining as shown in table 4 and Fig. 6.Simultaneously
The simulation result giving PSCAD software is contrasted, and accurate solution therein is to be obtained under 1 μ s step-length using PSCAD software
's.
Table 4 inductive drop
Above example is only not intended to limit in order to technical scheme to be described, although with reference to above-described embodiment pair
The present invention has been described in detail, and those of ordinary skill in the art still can enter to the specific embodiment of the present invention
Row modification or equivalent, these without departing from any modification of spirit and scope of the invention or equivalent, all in application
Within the claims of the pending present invention.
Claims (13)
1. a kind of on-off circuit electromagnetic transient analysis method is it is characterised in that described analysis method includes：
S1, according to switch circuit topology build circuit state equation；
S2, receive switch motion information after, change the state equation of circuit topology changing；
S3, receive switch motion information after, reinitialize each node potential of circuit；
The state equation of the circuit of modification after S4, solution switch motion；
S5：On-off circuit transient analysis is carried out according to the quantity of state in calculated each moment.
2. on-off circuit transient analysis method as claimed in claim 1 is it is characterised in that state equation in described step S1
Build and include：
(1-1) digitization of circuit topology：Node to circuit network and branch number select ground reference node；
(1-2) determine coefficient matrix：
Define n+1 rank neutral element square formation KR、KLAnd KC, and n+1 rank neutral element vector Is；
Branch road execution false code circulation, and coefficient square formation and vectorial depression of order are processed as n rank；
(1-3) coefficient matrix and Circuits System equation is used to build the circuit state equation shown in following formula (1)：
3. on-off circuit electromagnetic transient analysis method as claimed in claim 2 is it is characterised in that the circulation of described false code is wrapped
Include：
(1.1) it is calculated as follows resistance branch：
(1.2) then it is calculated as follows inductive branch：
(1.3) it is calculated as follows capacitive branch：
(1.4) it is calculated as follows voltage source branch road and the positive pole of voltage source is connected with node j：
(1.5) it is calculated as follows current source branch and the forward direction of current source points to node j's by node i：
Wherein, Rs：Ideal voltage source internal resistance value；R：The resistance value of resistance branch；L：The inductance value of inductive branch；C：Capacitive branch
Capacitance；Us：The output voltage values of ideal voltage source branch；Is：The output current value of current source branch.
4. on-off circuit electromagnetic transient analysis method as claimed in claim 2 it is characterised in that described Circuits System equation such as
Shown in following formula：
In formula,It is n rank column vector,The current potential of corresponding node n；KR、KLAnd KC：It is respectively n level
Matrix number；N rank power supply column vector；
Coefficient matrix K1、K2, R and x as follows：
E is unit diagonal matrix；
5. on-off circuit transient analysis method as claimed in claim 1 is it is characterised in that coefficient matrix shown as the following formula is repaiied
Change t in described step S20State equation after moment switch motion：
Wherein, Kr:The equivalent conductance matrix of switching branches, removes
WithOutward, KrIn other elements other be zero；KR,+：Resistance coefficient matrix before switch motion；KR,-：Open
Resistance coefficient matrix after the action of pass.
6. on-off circuit transient analysis method as claimed in claim 1 is it is characterised in that the initialization again described in step S3 is grasped
It is shown below：
Wherein,Node potential integration in time
Amount；Is,d+：The Norton equivalent electric current source information of ideal voltage source；Δt0=td+-td-：Minimum time step；
xd+And xd-：Represent t respectivelyd+And td-The quantity of state in moment.
7. on-off circuit transient analysis method as claimed in claim 1 it is characterised in that in step S4 circuit state equation
With the Iteration Recursive Solution shown in following formula：
Wherein, Δ t is the time step between moment n and moment n+1；β is an alternative coefficient；RnIt is that moment n institute is right
The input vector answered, Rn+1It is the input vector corresponding to the n+1 moment.
8. the on-off circuit transient analysis method as shown in claim 7 is it is characterised in that described alternative factor beta can
Value includes：β=0, is front to Euler method；β=0.5, is trapezoidal method；Or, β=1, for backward Euler method.
9. on-off circuit transient analysis method as claimed in claim 1 is it is characterised in that shape according to each moment calculating
State amount obtains simulation curve, carries out on-off circuit transient analysis.
10. a kind of analytical equipment of described analysis method as arbitrary in claim 1-9 is it is characterised in that described analytical equipment bag
Include：Establishing equation module, adjusting module, initialization module, on-off circuit solve module and switching transients analysis module；
Described establishing equation module builds state equation according to circuit topology figure, and receiving circuit switch motion information；
Described adjusting module adjusts the coefficient of state equation after described establishing equation module receives contactor action message
Matrix；
Described initialization module initializes node potential, and according to the capacitance voltage in circuit and inductive current, node potential is entered
Row weight initialization operation；
Described on-off circuit solves module immediate integration Recursive Solution state equation；
Described switching transients analysis module carries out on-off circuit transient analysis according to the quantity of state in calculated each moment.
11. analytical equipments as claimed in claim 10 it is characterised in that described establishing equation module include digitization module,
Loop module and matrix generation module；
Circuit topology information is stored in a computer by described digitization module with digitization form；
Described loop module includes resistance branch, inductive branch, capacitive branch, voltage source branch road and current source branch cycle calculations
False code；
Described matrix generation module eliminates the 0th row and the 0th row of each coefficient matrix, generates n rank square formation.
12. analytical equipments as claimed in claim 11 are it is characterised in that the function of described digitization module includes：
(1) node serial number to circuit network, and select ground reference node；
(2) branch number to circuit, and stored in a computer with the form sequentially forming digitization of branch number；
(3) build the system equation of circuit topology.
13. analytical equipments as claimed in claim 11 it is characterised in that comprise in described matrix generation module state equation and
Coefficient matrix corresponding relation between system equation, is shown below：
Wherein, E is unit diagonal matrix.
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