CN108462182B - A kind of Three-Phase Transformer method for establishing model based on electrical quantity transformation matrix - Google Patents
A kind of Three-Phase Transformer method for establishing model based on electrical quantity transformation matrix Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The invention discloses a kind of Three-Phase Transformer method for establishing model based on electrical quantity transformation matrix, comprising the following steps: establishes the original admittance matrix Y of three-phase transformerp, and Y is modified according to the former vice-side winding connection type of three-phase transformerpThe no-load voltage ratio of battle array；The voltage transformation Matrix C of primary side is determined according to primary side connection typep；C is determined according to the former secondary side mode of connectionspAnd Cps；The voltage transformation Matrix C on secondary side is determined according to group labelsAnd modify Cps；The voltage transformation Matrix C and current transformation matrix G of transformer are formed according to each submatrix of transformer voltage transformation matrix；According to YpBattle array and transformation matrix derive three-phase transformer node admittance matrix YTn.The present invention solves the problems, such as that relational matrix analysis is not suitable for seeking for the node admittance matrix of certain connection group transformers, further simplifies the workload of software programming and reduces the probability of error, improves the accuracy for seeking three-phase transformer triphase flow.
Description
Technical field
The present invention relates to a kind of method for building up of Three-Phase Transformer model, especially a kind of power distribution network three-phase power flow institute
The triphase flow method for building up of the distribution three-phase transformer used.
Background technique
Distribution system is by distribution line, distribution transformer, distribution pressure regulator, panel switches, distribution capacitor and distribution
The direct network system that electric energy is distributed to terminal user of the compositions such as load.Power System Analysis is carried out firstly the need of to being
Each element establishes suitable model in system.It is different from the three-phase symmetrical method of operation of grid, the load of power distribution network and
Network all may be asymmetric, when power distribution network carries out Load flow calculation, the characteristics of being considered as asymmetrical three-phase, carries out Three-phase Power Flow meter
It calculates.Therefore power distribution network three-phase power flow needs to establish the triphase flow of each element of distribution network.
The three-phase transformer model of single-phase Load flow calculation uses transformer single phase model, and people are generally only concerned transformer change
Than and impedance.But in power distribution network three-phase power flow, transformer model is more complex, not only to consider transformer voltage ratio,
The problems such as whether connection type of transformer winding is grounded with connection group and neutral point be also concerned about.The original of three-phase transformer
Respectively there are 3 windings while with secondary, the head end of three-phase windings and end are attached to and are drawn three-phase head end, there are two types of connection sides
Formula: one is one end of three-phase transformer three-phase windings is connected together, the other end is drawn, and referred to as three-phase transformer star connects
It connects；Another kind is that the head end of a phase winding and another phase winding end are successively connected into triangle, referred to as three-phase transformer three
Angle connection.
The former vice-side winding of three-phase transformer is likely to be connected into star or triangle, national regulations: three-phase transformer around
When group is star-like connection, marked as Y (primary side winding) and y (vice-side winding), when neutral point is drawn, marked as YN or yn；Winding
When being connected for triangle, marked as D (primary side winding) and d (vice-side winding).
Since the former vice-side winding of three-phase transformer is likely to be connected into star or triangle, the secondary side of the original of three-phase transformer
The different connections of winding, available multiple combinations, wherein delta connection can be divided into left lateral wiring and right lateral wiring, and star connects
The neutral point of method be divided into again ground connection and it is earth-free.After the combination of these connection types, 16 kinds of combinations can be obtained.
The polarity possibility of three-phase transformer original vice-side winding is identical may also be on the contrary, so polarity be closed there are two types of every kind of combinations
System.
Three-phase transformer original vice-side winding is each may mutually to be corresponded, i.e. A, B, C of primary side winding correspond respectively to pair
A, b, c of side winding, corresponding winding is in same iron core column；Three-phase transformer original vice-side winding is each may not also mutually to be corresponded to,
That is the A of primary side winding corresponds to the b phase or c phase of vice-side winding, but to meet positive phase sequence between the three-phase voltage of vice-side winding
Relationship, therefore corresponding 3 kinds of phase relations of every kind of polarity.
Therefore there are 6 kinds of phase relations under every kind of connection combination of three-phase transformer, then 16 kinds of combinations share 96
Kind connection group.
The number that three-phase transformer connects group label indicates that new national standard is using former secondary side using the clock ordinal number of phase difference
The phase difference of corresponding phase voltage phasor judges, is the corresponding phase in secondary side with reference to being directed toward 0 point of clock with the phase voltage phasor of primary side
Hour number is three-phase transformer connection group label when pointed by voltage phasor, and the dummy neutral of triangle is triangle
Center.It is 0,2,4,6,8,10 point of even number point wiring when three-phase transformer two sides all use identical connection type, i.e. Yy, Dd；
It is 1,3,5,7,9,11 point of surprise when three-phase transformer side uses delta connection, i.e. Yd, Dy using the star-star connection other side
Several wiring.Transformer winding delta connection can obtain the group label of a certain requirement using left lateral wiring or right lateral wiring
Connection group, and effect is identical.Connection group needs not distinguish between the left lateral wiring of delta connection under normal circumstances or right lateral connects
Line, but to consider the difference whether neutral point of star-star connection is grounded, such transformer connection group is reduced to 54 kinds.
When three-phase transformer models, consider that voltage change when three-phase transformer operates normally is little, thus energized circuit
Consumption changed power it is little, can merge with the power of load, it is unified to consider.Therefore three-phase transformer modeling does not include generally
Energized circuit.
In power transmission network, since three-phase load and network are all symmetrical, the voltage (or electric current) of transmission system everywhere
It is symmetrically, i.e., three-phase voltage (or electric current) is equal in magnitude, and 120 ° of phase phase difference between two-phase voltage (or electric current), B phase is stagnant
120 ° of A phase afterwards, C phase lag 120 ° of B phase.When analytical calculation, the voltage of a certain phase (such as A phase) can be calculated with single-phase equivalent circuit
The voltage (or electric current) of (or electric current), other two-phases directly writes out result according to symmetric relation.Three phase transformations in single-phase equivalent circuit
Depressor model only has transformer voltage ratio and equivalent impedance.
In power distribution network, since three-phase load and network are asymmetric, the voltage (or electric current) of distribution system everywhere is also not
Symmetrically, when analytical calculation, it is necessary to use three-phase circuit model, calculate together.The three-phase transformer mould in three-phase equivalent circuit
Type will not only consider transformer voltage ratio and equivalent impedance, it is also contemplated that the primary side winding of transformer and the wiring of vice-side winding and group
Not.
The method for building up of Three-Phase Transformer model has two methods of symmetrical component method and relational matrix analysis.If transformer three
Phase parameter is symmetrical, more convenient using symmetrical component method；If Three-Phase Transformer parameter unbalance, three sequences cannot be decoupled, and be used
Symmetrical component method is with regard to highly difficult.Relational matrix analysis establish Three-Phase Transformer model then with the whether symmetrical nothing of Three-Phase Transformer parameter
It closes, and establishment process succinctly facilitates, is conducive to program and realizes, the Three-Phase Transformer method for establishing model of existing method based on correlation matrix
It is as follows:
Three-Phase Transformer model, can be with the function of load as shown in Figure 1, wherein the consumption changed power of energized circuit is little
Rate merges, unified to consider.Therefore Three-Phase Transformer modeling does not include the parameter G of energized circuit generallyT, only consider series admittance YT
Modeling.
Three-phase transformer usually has a public iron core, thus intercouples between each winding.Three-phase transformer three-phase around
The voltage vector U of group branchbWith current vector IbBetween relationship can be retouched by the original admittance matrix of three-phase transformer
It states, such as following formula:
Ib=YpUb (1)
In formula,It is transformer winding branch current column vector,Transformer winding branch voltage column vector, subscript 1,2,3 indicate primary side around
Group, subscript 4,5,6 indicate vice-side winding, YpIt is the original admittance matrix of three-phase transformer, indicates are as follows:
In formula, every equal value admittance of three-phase transformer are as follows:
Y=1/z=1/ (r+jx) (3)
In formula, z, r and x are respectively the equivalent impedance, substitutional resistance and equivalent leakage reactance of the every phase winding of three-phase transformer.
Consider the model of the non-standard no-load voltage ratio of three-phase transformer as shown in Figure 2, the original admittance matrix Y of three-phase transformerp
It indicates are as follows:
In formula, α0The non-standard no-load voltage ratio of primary side winding, be primary side winding voltage rating and primary side phase voltage a reference value it
Than β0It is the non-standard no-load voltage ratio of vice-side winding, is the ratio between vice-side winding voltage rating and secondary side phase voltage a reference value.
In practical distribution network, the non-standard no-load voltage ratio of the equivalent star-like connection of three-phase transformer be it is known, it is with three
The relationship of the non-standard no-load voltage ratio of phase transformer winding is as follows:
When primary side is that star (neutral ground or earth-free) connects, are as follows:
α0=α (5)
In formula, α is the non-standard no-load voltage ratio of the equivalent star-like connection of primary side of three-phase transformer, be primary side phase voltage rated value with
The ratio between primary side phase voltage a reference value.
When primary side is that triangle connects, are as follows:
When secondary side is that star (neutral ground or earth-free) connects, are as follows:
β0=β (7)
In formula, β is the non-standard no-load voltage ratio of the equivalent star-like connection in secondary side of three-phase transformer, for secondary side phase voltage rated value with
The ratio between secondary side phase voltage a reference value.
When secondary side is that triangle connects, are as follows:
Load flow calculation uses node voltage UnWith node injecting power (or Injection Current In), it is three phase-change pressures of reflection
The node voltage U of each endpoint of devicenWith node Injection Current InBetween relationship.
In=YTnUn (9)
In formula,It is the node current column vector of each endpoint of three-phase transformer,It is the node voltage column vector of each endpoint of three-phase transformer, subscript A, B, C table
Show that the node that primary side winding is connected, subscript a, b, c indicate the node that vice-side winding is connected, YTnIt is the node of three-phase transformer
Admittance matrix.
Three-phase transformer admittance matrix Y in formula (1)pIt is three-phase branch voltage U inside reflection three-phase transformerbWith branch electricity
Flow IbBetween relationship admittance matrix, pass through YpIt can derive that reflection three-phase transformer is respectively held with three-phase transformer connection relationship
The node voltage U of pointnWith node Injection Current InBetween relationship node admittance matrix YTn。
If three-phase transformer branch voltage UbWith node voltage UnBetween relationship are as follows:
Ub=CUn (10)
In formula, C is branch voltage UbWith node voltage UnIncidence matrix, referred to as voltage incidence matrix.
In view of branch current I under normal conditionsbWith node current InElectric current incidence matrix G be voltage incidence matrix C
Transposition.Therefore, node admittance matrix can be found out by original admittance matrix, are as follows:
YTn=CTYpC (11)
In formula, the transposition of subscript T representing matrix.
The node admittance of three-phase transformer is established for the three-phase transformer equivalent circuit of Dyn11 wiring as shown in Figure 3
Matrix.
The three-phase transformer incidence matrix C of Dyn11 wiring are as follows:
The primary side of Dyn11 wiring transformer is triangle connection, is hadSecondary side is the star of neutral ground
Connection, there is β0=β.Transformer voltage ratio is substituted into formula (4), obtains the original admittance matrix Y of transformerpAre as follows:
The node admittance matrix Y of three-phase transformer is obtained by formula (11)TnAre as follows:
Three-phase transformer is connected with 96 kinds of combinations, it is common have it is ten several.It can prove the other three-phase transformation of same connection group
The node admittance matrix of device be it is identical, the transformer primary pair side mode of connection have YNyn, YNy, YNd, Yyn, Yy, Yd, Dyn, Dy,
Dd totally 9 kinds of combinations, every kind of combination has 6 kinds of group labels again, total to share 54 kinds of connection groups, also very much.Work out power distribution network three
Phase flow calculation program, it is necessary to consider all these combinations, writes out respective incidence matrix, the model inference that this 54 kinds are combined
Out, i.e., the formula of the transformer node admittance matrix of these combinations is write out.The Three-Phase Transformer model of such multiple types
It is comparatively laborious all using derivation by hand, and it is easy error.Pertinent literature only provides the other three-phase transformation of a part of typical connection group
Device node admittance matrix, and it is how wrong.In order to design perfect power distribution network three-phase power flow program, the person that needs programming
Oneself derive the triphase flow of these other transformers of connection group one by one by hand, it is very inconvenient, it is also difficult to guarantee derived change
The accuracy of depressor triphase flow.Therefore, Chinese patent CN201610579878.4 proposes a kind of distribution three-phase transformer three-phase
Model automatic forming method can make full use of Matlab distinctive the characteristics of being good at matrix operation and complex operation, utilize symbol
Number operation automatic deduction goes out the node admittance matrix model of three-phase transformer, solves and derives distribution three-phase transformer three-phase by hand
The time-consuming and laborious problem of model, improves the efficiency for seeking three-phase transformer triphase flow.But Chinese patent CN
201610579878.4 used incidence matrix is more when method exports the node admittance matrix model of three-phase transformer, compare
Complexity is easy error when programming, still needs to be advanced optimized and simplified modeling procedure.In addition, using traditional relational matrix analysis
Also can not direct derivation go out transformer primary vice-side winding and led using the node of three-phase transformer of isolated neutral star-star connection
Receive matrix.
Summary of the invention
To solve the above problems existing in the prior art, the present invention will propose a kind of transformation based on electrical quantity transformation matrix
Device triphase flow method for building up, to advanced optimize and simplify modeling procedure, so that the modeling of three-phase transformer triphase flow
Process is more succinct, improves the efficiency and correctness of programming.
Technical scheme is as follows: a kind of Three-Phase Transformer method for establishing model based on electrical quantity transformation matrix,
The different connections for organizing other transformer transformation matrix under the identical connection type in transformer primary pair side are established, by a basic electrical quantity
Transformation matrix directly writes out the transformation matrix of different group transformers under same connection type, then derives Three-Phase Transformer mould
Type.
It defines primary side clock and secondary side clock is as follows: assuming that three-phase transformer primary side winding presses the arrangement of AX, BY, CZ sequence simultaneously
If positive polarity then defines transformer connection group of the primary side using star-star connection when marked as secondary side clock in the side head end A, B, C.
The secondary side clock for such as connecting the transformer that group is Yd1 is 1.Under above-mentioned assumed condition, if the terminal X of primary side winding, terminal Y
Star-like connection is connected together into terminal Z, then defining primary side clock is 0；If primary side is connected using triangle, terminal A and end
Sub- Z, terminal B and terminal X, terminal C and terminal Y are separately connected, then defining primary side clock is 1.Transformer bank type is marked as transformation
The difference of device pair side clock and primary side clock, transformer secondary clock are the sum of transformer bank type label and primary side clock, are such as obtained
Transformer secondary clock be greater than or equal to 12, then subtract 12 as secondary side clocks.
For the sake of easy analysis, if transformer primary winding uses neutral ground star-like connection as shown in Figure 4, neutrality
The earth-free star-like connection of point or triangle connection, primary side clock is respectively 0,0 or 1.
When YNd wiring being discussed below according to Fig. 5, different connection group transformers under the identical mode of connection in transformer primary pair side
Secondary side incidence matrix the characteristics of.
As shown in figure 5, when transformer uses YNd wiring and primary side clock as 0 neutral ground star-star connection, primary side around
The incidence matrix of group branch voltage and node voltage are as follows:
The transformer bank type label of YNd wiring can be 1,3,5,7,9,11, and corresponding transformer secondary clock is also distinguished
It is 1,3,5,7,9,11, it is identical as transformer bank type label.As shown in figure 5, the vice-side winding branch of different connection group transformers
The incidence matrix of road voltage and node voltage is respectively as follows:
Transformer secondary clock label is designated as under each matrix in formula (16)-(21).
Observation type (16)-(21), can obtain Cs5By Cs1The 2nd column, the 3rd column and the 1st column composition, Cs9By Cs1The 3rd column, the 1st
Column and the 2nd column composition, Cs7=-Cs1, Cs3=-Cs9, Cs11=-Cs5.In this way, it is only necessary to set Cs1, other secondary side clocks are corresponding
Secondary voltage incidence matrix can be by Cs1It obtains, reduces the number for needing the secondary voltage incidence matrix being arranged.
The relationship of the voltage incidence matrix for the vice-side winding wiring that secondary side clock is even number can similarly be obtained are as follows: Cs4By Cs0's
2nd column, the 3rd column and the 1st column composition, Cs8By Cs0The 3rd column, the 1st column and the 2nd column composition, Cs6=-Cs0, Cs2=-Cs8, Cs10
=-Cs4。
According to transformer secondary clock, the voltage incidence matrix C on secondary side is determined by formula (16)-(21)s, the electricity of YNd1 can be obtained
Press incidence matrix are as follows:
The voltage incidence matrix for each group three-phase transformer that former secondary side wiring is YNyn, YNd, Dyn, Dd can be similarly obtained,
It can derive that former secondary side wiring is each group three-phase transformer of YNyn, YNd, Dyn, Dd using traditional relational matrix analysis
Node admittance matrix.Wherein voltage incidence matrix has following form:
In formula, O is 3 × 3 rank null matrix.
Former pair side wiring is that the node admittance matrix of the three-phase transformer of YNy, Yy, Yyn, Yd, Dy then can not be directly by closing
Connection matrix method is derived.The present invention proposes the node admittance matrix that this 5 kinds of transformers are derived with electrical quantity Transformation Matrix Method.Electricity
Tolerance transformation matrix reflects the transformation relation of two electrical quantity, including voltage transformation matrix and current transformation matrix, incidence matrix
It is considered as the special case of transformation matrix.The element of incidence matrix only has 0,1, -1, and the element of transformation matrix can be any real number.
The electrical quantity transformation matrix of these types of situation is released below.
(1) transformer of the transformer of Dy wiring and Yd wiring
If the transformer secondary isolated neutral of Dyn11 wiring shown in Fig. 3 is exactly the transformer of Dy11 wiring, ginseng
Examine the electrical quantity transformation matrix that equivalent circuit shown in Fig. 3 derives the three-phase transformer that wiring is Dy11.
The neutral point voltage on the three-phase transformer pair side of Dy11 wiring is not 0, if considering secondary side neutral point voltage's
Voltage incidence matrix is C ', then the relational expression of transformer winding branch voltage and node voltage are as follows:
It is obtained by formula (24)Are as follows:
According to symmetrical component method, it is known that without residual voltage, vice-side winding in the vice-side winding of the three-phase transformer of Dy wiring
The sum of voltage is 0, is obtained by formula (25):
Formula (26) substitutes into formula (24), obtains:
C is being not voltage incidence matrix in formula (27), referred to as voltage transformation matrix, due to voltage transformation matrix and voltage
Incidence matrix is there are many identical property and voltage incidence matrix is considered as the special case of voltage transformation matrix, therefore is still indicated with C
Voltage transformation matrix.The voltage transformation Matrix C of the three-phase transformer of Dy11 wiring are as follows:
The constraint condition that the sum of three-phase current in view of earth-free star-star connection is 0, can derive Dy11 wiring three
The current transformation matrix of phase transformer is the transposition of voltage transformation matrix.
It can similarly derive the voltage transformation matrix of the three-phase transformer of Yd1 wiring are as follows:
The current transformation matrix of the three-phase transformer of Yd1 wiring is also the transposition of voltage transformation matrix.
(2) transformer of Yy wiring
Wiring is derived by taking the three-phase transformer equivalent circuit of Yy0 wiring as shown in FIG. 6 as an example as the three-phase transformer of Yy
Electrical quantity transformation matrix.
The neutral point voltage on the secondary side of the original of the three-phase transformer of Yy0 wiring is not 0, if considering primary side neutral point voltageWith secondary side neutral point voltageVoltage incidence matrix be C ', the then relationship of transformer winding branch voltage and node voltage
Formula are as follows:
It is obtained by formula (30)WithAre as follows:
According to symmetrical component method, it is known that without residual voltage, primary side in the former vice-side winding of the three-phase transformer of Yy0 wiring
The sum of winding voltage and the sum of vice-side winding voltage are all 0, are obtained by formula (31):
Formula (32) substitutes into formula (30), obtains:
It is obtained by formula (33), the voltage transformation Matrix C of Yy0 wiring three-phase transformer are as follows:
Consider that the sum of three-phase current of earth-free star-star connection is 0 constraint condition, can derive three phase transformation of Yy0 wiring
The current transformation matrix of depressor is the transposition of voltage transformation matrix.
(3) transformer of the transformer of YNy wiring and Yyn wiring
If the transformer primary side neutral ground of Yy0 wiring shown in fig. 6 is exactly the transformer of YNy0 wiring, with reference to figure
Equivalent circuit shown in 6 derives the electrical quantity transformation matrix of the three-phase transformer of YNy0 wiring.
The secondary side neutral point voltage of the three-phase transformer of YNy0 wiring is not 0, if considering secondary side neutral point voltage's
Incidence matrix is C ', then the relational expression of transformer winding branch voltage and node voltage are as follows:
It is obtained by formula (35)Are as follows:
According to symmetrical component method, it is known that the primary side of the three-phase transformer of YNy wiring has zero sequence access, if primary side node electricity
Briquetting contains residual voltage, then has zero-sequence current to flow through energized circuit, residual voltage can be generated in transformer primary vice-side winding, former
The sum of vice-side winding voltage is not 0.There are following relationships for YNy wiring transformer original vice-side winding branch voltage:
It is obtained by formula (35):
Formula (37) and formula (38) substitute into formula (36), obtain:
Formula (39) substitutes into formula (35), obtains:
Voltage transformation Matrix C is obtained by formula (40) are as follows:
The constraint condition that the sum of three-phase current in view of earth-free star-star connection is 0, YNy0 wiring three-phase transformer
Current transformation matrix are as follows:
For the three-phase transformer of YNy wiring, current transformation matrix is still block diagonal matrix, and voltage transformation matrix is then not
It is block diagonal matrix, voltage transformation matrix has following form:
Yyn wiring is derived by taking the three-phase transformer equivalent circuit of Yyn0 wiring and Yyn6 wiring as shown in Figure 7 as an example
The electrical quantity transformation matrix of three-phase transformer.
The primary side neutral point voltage of the three-phase transformer of Yyn0 wiring is not 0, if considering primary side neutral point voltage's
Voltage incidence matrix is C ', then the relational expression of transformer winding branch voltage and node voltage are as follows:
It is obtained by formula (44)Are as follows:
According to symmetrical component method, it is known that there is zero sequence access on the secondary side of the three-phase transformer of Yyn wiring, if secondary mid-side node electricity
Briquetting contains residual voltage, then has zero-sequence current to flow through energized circuit, residual voltage can be generated in transformer primary vice-side winding, former
The sum of vice-side winding voltage is not 0.There are following relationships for Yyn wiring transformer original vice-side winding branch voltage:
It is obtained by formula (44):
Formula (46) and formula (47) substitute into formula (45), obtain:
Formula (48) substitutes into formula (44), obtains:
Voltage transformation Matrix C is obtained by formula (49) are as follows:
The constraint condition that the sum of three-phase current in view of earth-free star-star connection is 0, Yyn0 wiring three-phase transformer
Current transformation matrix are as follows:
The primary side neutral point voltage of the three-phase transformer of Yyn6 wiring is not 0, if considering primary side neutral point voltage's
Voltage incidence matrix is C ', then the relational expression of transformer winding branch voltage and node voltage are as follows:
The primary side neutral point voltage of the three-phase transformer of Yyn6 wiringAlso distinguish with former vice-side winding branch voltage relationship
For formula (45) and formula (46), obtained by formula (52):
Formula (46) and formula (53) substitute into formula (45), obtain:
Formula (54) substitutes into formula (52), obtains:
Voltage transformation Matrix C is obtained by formula (55) are as follows:
The constraint condition that the sum of three-phase current in view of earth-free star-star connection is 0, Yyn6 wiring three-phase transformer
Current transformation matrix are as follows:
For the three-phase transformer of Yyn wiring, current transformation matrix is still block diagonal matrix, and voltage transformation matrix is then not
It is block diagonal matrix, voltage transformation matrix has following form:
C in formula (58)psMatrix element when Yyn wiring and when secondary side clock is 0,4,8 be positive value；When Yyn wiring and
It is negative value when secondary side clock is 2,6,10；Other situations are zero.
By original admittance matrix YpThree-phase transformer node admittance matrix Y is derived with transformation matrix C and GTnAre as follows:
YTn=GYpC (59)
To the three-phase transformer of all types wiring, current transformation matrix is all block diagonal matrix, voltage transformation matrix
It is then not all block diagonal matrix, it is as follows that voltage transformation matrix is write as Unified Form:
Current transformation matrix are as follows:
For the identical transformer primary pair side mode of connection, C in formula (60)p、CspIt is all identical, Cps、CsThen with wiring group
Label is related.It is similar with secondary voltage incidence matrix feature, the transformer of different group labels under the identical former secondary side mode of connection
Secondary voltage transformation matrix CsIt connects each other, CpsThen there is only the differences of sign.In this way, it is only necessary to set a base
This secondary voltage transformation matrix Cs0, the secondary voltage transformation matrix of other group labels can be by Cs0It obtains, reducing needs
The number for the secondary voltage transformation matrix to be arranged.
A kind of Three-Phase Transformer method for establishing model based on electrical quantity transformation matrix, comprising the following steps:
A, transformer primary winding connection type k is read1, vice-side winding connection type k2, transformer connect group label k3,
Primary side no-load voltage ratio variable α and pair side no-load voltage ratio variable β are set.
The primary side winding mode of connection k of three-phase transformer1There are tri- kinds of YN, Y, D, vice-side winding mode of connection k2There are yn, y, d
Three kinds.Transformer connects group label k3Related with former secondary side wiring combination, former pair side wiring is YNyn, YNy, Yyn, Yy, Dd
K when five kinds of wiring combinations3It is 0,2,4,6,8,10；K when former pair side wiring is tetra- kinds of wiring combinations of YNd, Yd, Dyn, Dy3For 1,3,
5,7,9,11.α is the non-standard no-load voltage ratio of the equivalent star-like connection of primary side of three-phase transformer, is primary side phase voltage rated value and primary side
The ratio between phase voltage a reference value, β are the non-standard no-load voltage ratios of the equivalent star-like connection in secondary side of three-phase transformer, specified for secondary side phase voltage
The ratio between value and secondary side phase voltage a reference value.
B, it establishes the voltage transformation matrix for reflecting three-phase transformer winding branch voltage and node voltage relationship and one normal
Matrix number.
Voltage transformation matrix is respectively as follows:
In formula, CYNVoltage transformation matrix of the clock for 0 ground connection star-star connection when, C are used for original/vice-side windingYFor it is former/
Vice-side winding uses voltage transformation matrix of the clock for 0 earth-free star-star connection when, CDFor original/vice-side winding use clock for
Voltage transformation matrix when 1 delta connection.
One scalar matrix are as follows:
C, the original admittance matrix Y of three-phase transformer shown in formula (4) is establishedp, and according to the secondary side of the original of three-phase transformer
Winding connection modifies Y by formula (5)-(8)pThe no-load voltage ratio of battle array.
D, C is setps0、CspFor 3 × 3 rank matrixes, and it is initialized as null matrix；
E, judge whether to meet k1For Y and k2For yn, if being unsatisfactory for going to step G；
F, C is enabledps0=(α/β) P, goes to step I；
G, judge whether to meet k1For YN and k2For y, if being unsatisfactory for going to step I；
H, C is enabledsp=(beta/alpha) P；
I, judge k1It whether is YN, if being unsatisfactory for going to step K；
J, C is enabledp=CYN, p=0, go to step N；
K, judge k1It whether is Y, if being unsatisfactory for going to step M；
L, C is enabledp=CY, p=0, go to step N；
M、Cp=CD, p=1；
N, judge k2It whether is yn, if being unsatisfactory for going to step P；
O, C is enableds0=CYN, go to step S；
P, judge k2It whether is y, if being unsatisfactory for going to step R；
Q, C is enableds0=CY, go to step S；
R、Cs0=CD；
S, group label k is connected according to transformer3Pair side clock k is determined with primary side clock p0For
k0=mod (k3+p,12) (66)
In formula, mod is Matlab MOD function, obtains k3+ p is divided by the remainder after 12.
T, according to k0Determine the voltage transformation Matrix C of transformer secondarysAnd Cps；
Determine the voltage transformation Matrix C of transformer secondarysAnd CpsThe step of it is as follows:
T1, transformer secondary clock k is read0；
T2, judge whether to meet k0Equal to 0 or k0Equal to 1, if being unsatisfactory for going to step T4；
T3, C is enableds=Cs0, Cps=Cps0；
T4, judge whether to meet k0Equal to 2 or k0Equal to 3, if being unsatisfactory for going to step T6；
T5, C is enableds=-Cs0(:, [3,1,2]), i.e., successively take Cs0The 3rd column, the 1st column and the 2nd column, and after taking opposite number,
It is assigned to Cs, and set Cps=-Cps0；
T6, judge whether to meet k0Equal to 4 or k0Equal to 5, if being unsatisfactory for going to step T8；
T7, C is enableds=Cs0(:, [2,3,1]), Cps=Cps0；
T8, judge whether to meet k0Equal to 6 or k0Equal to 7, if being unsatisfactory for going to step T10；
T9, C is enableds=-Cs0, Cps=-Cps0；
T10, judge whether to meet k0Equal to 8 or k0Equal to 9, if being unsatisfactory for going to step T12；
T11, C is enableds=Cs0(:, [3,1,2]), Cps=Cps0；
T12, judge whether to meet k0Equal to 10 or k0Equal to 11, if being unsatisfactory for going to step U；
T13, C is enableds=-Cs0(:, [2,3,1]), Cps=-Cps0；
U, the voltage transformation of transformer is formed by formula (60) and formula (61) according to each submatrix of transformer voltage transformation matrix
Matrix C and current transformation matrix G；
V, according to original admittance matrix YpThree-phase transformer node is derived by symbolic operation by formula (59) with transformation matrix to lead
Receive matrix YTn。
Compared with prior art, the invention has the following advantages:
1, the Three-Phase Transformer method for establishing model proposed by the present invention based on electrical quantity transformation matrix, solves association square
The node admittance matrixes that the tactical deployment of troops is not suitable for certain connection group transformers seek problem.The present invention is deduced identical former secondary
The electrical quantity transformation matrix of the transformer of different group labels connects each other under the mode of connection of side, reduces what needs were arranged
The number of electrical quantity transformation matrix；The concept for proposing and utilizing transformer primary pair side clock, is further simplified the work of software programming
Work amount and the probability for reducing error, improve the accuracy for seeking three-phase transformer triphase flow.
2, the present invention guarantees to derive using the node admittance matrix model of the symbolic operation automatic deduction transformer of Matlab
As a result correctness solves the problems, such as that derivation distribution three-phase transformer triphase flow is bothersome laborious by hand and is easy error, mentions
The high efficiency for seeking three-phase transformer triphase flow.
Detailed description of the invention
The present invention shares attached drawing 9 and opens, in which:
Fig. 1 is three-phase transformer triphase flow figure.
Fig. 2 is the single phase model figure for considering the non-standard no-load voltage ratio of three-phase transformer.
Fig. 3 is the three-phase transformer equivalent circuit diagram of Dyn11 wiring.
Fig. 4 is the wiring diagram for defining transformer primary side clock.
Fig. 5 is the three-phase transformer equivalent circuit diagram of different group YNd wiring.
Fig. 6 is the three-phase transformer equivalent circuit diagram of Yy0 wiring.
Fig. 7 is the three-phase transformer equivalent circuit diagram of Yyn0 wiring and Yyn6 wiring.
Fig. 8 is main flow chart of the invention.
Fig. 9 is that the present invention forms transformer secondary voltage transformation matrix procedures figure.
Specific embodiment
Transformer of the invention is further illustrated by taking the three-phase transformer of Yyn0 and Yyn6 wiring as an example with reference to the accompanying drawing
Triphase flow derivation process.
(1) the Three-Phase Transformer model inference of Yyn0 wiring
Fig. 7 is sought according to Fig. 8 and the Three-Phase Transformer method for establishing model shown in Fig. 9 based on electrical quantity transformation matrix
(a) the Three-Phase Transformer model of Yyn0 wiring shown in.Input transformer primary side connection type k1For Y, no-load voltage ratio α；Secondary side around
Group connection type k2For yn, no-load voltage ratio β；Transformer connects group label k3It is 0.
Operation result obtains the voltage transformation matrix of the three-phase transformer of Yyn0 wiring and current transformation matrix is respectively as follows:
Obtain the node admittance matrix Y of three-phase transformerTnAre as follows:
In formula, y is every equal value admittance of three-phase transformer.
(2) the Three-Phase Transformer model inference of Yyn6 wiring
For the transformer of Yyn6 wiring shown in Fig. 7 (b), input transformer primary side connection type k1For Y, no-load voltage ratio α；
Vice-side winding connection type k2For yn, no-load voltage ratio β；Transformer connects group label k3It is 6.
Operation result obtains the voltage transformation matrix of the three-phase transformer of Yyn6 wiring and current transformation matrix is respectively as follows:
Obtain the node admittance matrix Y of three-phase transformerTnAre as follows:
The present invention can be realized in any MATLAB programming language with symbolic operation function, but suggest use compared with new edition
This MATLAB language.
Claims (1)
1. a kind of Three-Phase Transformer method for establishing model based on electrical quantity transformation matrix, it is characterised in that: the following steps are included:
A, transformer primary winding connection type k is read1, vice-side winding connection type k2, transformer connect group label k3；
The primary side winding connection type k of three-phase transformer1There are tri- kinds of YN, Y, D, symbol YN, Y, D are respectively indicated in primary side winding
Property point ground connection star-like connection, isolated neutral star-like connection connected with triangle；Vice-side winding connection type k2There are yn, y, d
Three kinds, symbol yn, y, d respectively indicate the neutral ground star-like connection of vice-side winding, isolated neutral star-like connection and three
Angle connection；Transformer connects group label k3It is related with former secondary side wiring combination, former pair side wiring is YNyn, YNy, Yyn,
K when five kinds of wiring combinations of Yy, Dd3It is 0,2,4,6,8,10；K when former pair side wiring is tetra- kinds of wiring combinations of YNd, Yd, Dyn, Dy3
It is 1,3,5,7,9,11；
B, the voltage transformation matrix and a constant square of reflection three-phase transformer winding branch voltage and node voltage relationship are established
Battle array；
Voltage transformation matrix is respectively as follows:
In formula, CYNVoltage transformation matrix of the clock for 0 ground connection star-star connection when, C are used for original/vice-side windingYFor former/secondary side
Winding uses voltage transformation matrix of the clock for 0 earth-free star-star connection when, CDUse clock for 1 for original/vice-side winding
Voltage transformation matrix when delta connection；
Primary side clock and secondary side clock are defined as follows: assuming that three-phase transformer primary side winding is arranged and set by AX, BY, CZ sequence
Positive polarity then defines transformer connection group of the primary side using star-star connection when marked as secondary side clock in the side A, B, C；Above-mentioned vacation
If under the conditions of, terminal X, terminal Y and the terminal Z of primary side winding connect together into star-like connection, then defining primary side clock is 0；It is former
Side is connected using triangle, and terminal A and terminal Z, terminal B and terminal X, terminal C and terminal Y are separately connected, then when defining primary side
Clock is 1；For transformer bank type marked as the difference of transformer secondary clock and primary side clock, transformer secondary clock is transformer bank type
The sum of label and primary side clock when obtained transformer secondary clock is greater than or equal to 12, then subtract 12 as secondary side clock；
One scalar matrix are as follows:
C, the original admittance matrix Y of three-phase transformer is establishedp, and formula is pressed according to the former vice-side winding connection type of three-phase transformer
(7)-(10) Y is modifiedpThe no-load voltage ratio of battle array；
In formula, α0It is the non-standard no-load voltage ratio of primary side winding, is the ratio between primary side winding voltage rating and primary side phase voltage a reference value, β0
It is the non-standard no-load voltage ratio of vice-side winding, is the ratio between vice-side winding voltage rating and secondary side phase voltage a reference value, y is three-phase transformer
Every equal value admittance, expression formula are as follows:
Y=1/z=1/ (r+jx) (6)
In formula, z, r and x are respectively the equivalent impedance, substitutional resistance and equivalent leakage reactance of the every phase winding of three-phase transformer；
In practical distribution network, the non-standard no-load voltage ratio of the equivalent star-like connection of three-phase transformer is known, it and three phase transformations
The relationship of the non-standard no-load voltage ratio of depressor winding is as follows:
When primary side is neutral ground star or isolated neutral star-like connection, are as follows:
α0=α (7)
In formula, α is the non-standard no-load voltage ratio of the equivalent star-like connection of primary side of three-phase transformer, is primary side phase voltage rated value and primary side
The ratio between phase voltage a reference value；
When primary side is that triangle connects, are as follows:
When secondary side is neutral ground star or isolated neutral star-like connection, are as follows:
β0=β (9)
In formula, β is the non-standard no-load voltage ratio of the equivalent star-like connection in secondary side of three-phase transformer, to be secondary in phase voltage rated value and pair
The ratio between phase voltage a reference value；
When secondary side is that triangle connects, are as follows:
D, C is setps0、CspFor 3 × 3 rank matrixes, and it is initialized as null matrix；
E, judge whether to meet k1For Y and k2For yn, if being unsatisfactory for going to step G；
F, C is enabledps0=(α/β) P, goes to step I；
G, judge whether to meet k1For YN and k2For y, if being unsatisfactory for going to step I；
H, C is enabledsp=(beta/alpha) P；
I, judge k1It whether is YN, if being unsatisfactory for going to step K；
J, C is enabledp=CYN, p=0, go to step N；
K, judge k1It whether is Y, if being unsatisfactory for going to step M；
L, C is enabledp=CY, p=0, go to step N；
M、Cp=CD, p=1；
N, judge k2It whether is yn, if being unsatisfactory for going to step P；
O, C is enableds0=CYN, go to step S；
P, judge k2It whether is y, if being unsatisfactory for going to step R；
Q, C is enableds0=CY, go to step S；
R、Cs0=CD；
S, group label k is connected according to transformer3Pair side clock k is determined with primary side clock p0For
k0=mod (k3+p,12) (11)
In formula, mod is Matlab MOD function, obtains k3+ p is divided by the remainder after 12；
T, according to k0Determine the voltage transformation Matrix C of transformer secondarysAnd Cps；
Determine the voltage transformation Matrix C of transformer secondarysAnd CpsThe step of it is as follows:
T1, transformer secondary clock k is read0；
T2, judge whether to meet k0Equal to 0 or k0Equal to 1, if being unsatisfactory for going to step T4；
T3, C is enableds=Cs0, Cps=Cps0；
T4, judge whether to meet k0Equal to 2 or k0Equal to 3, if being unsatisfactory for going to step T6；
T5, C is enableds=-Cs0(:, [3,1,2]), i.e., successively take Cs0The 3rd column, the 1st column and the 2nd column, and after taking opposite number, assignment
To Cs, and set Cps=-Cps0；
T6, judge whether to meet k0Equal to 4 or k0Equal to 5, if being unsatisfactory for going to step T8；
T7, C is enableds=Cs0(:, [2,3,1]), Cps=Cps0；
T8, judge whether to meet k0Equal to 6 or k0Equal to 7, if being unsatisfactory for going to step T10；
T9, C is enableds=-Cs0, Cps=-Cps0；
T10, judge whether to meet k0Equal to 8 or k0Equal to 9, if being unsatisfactory for going to step T12；
T11, C is enableds=Cs0(:, [3,1,2]), Cps=Cps0；
T12, judge whether to meet k0Equal to 10 or k0Equal to 11, if being unsatisfactory for going to step U；
T13, C is enableds=-Cs0(:, [2,3,1]), Cps=-Cps0；
U, the voltage transformation Matrix C of transformer is formed by formula (12) and formula (13) according to each submatrix of transformer voltage transformation matrix
With current transformation matrix G；
In formula, O is 3 × 3 rank null matrix, the transposition of subscript T representing matrix；
V, according to original admittance matrix YpThree-phase transformer node admittance matrix is derived by symbolic operation by formula (14) with transformation matrix
YTn:
YTn=GYpC (14)
Terminate.
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