CN108718091A - A kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network - Google Patents
A kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network 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
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract
The present invention relates to a kind of linear tidal current computing methods of three-phase polar coordinate system applied to active distribution network, include the following steps：Step S1：The power distribution network node power equilibrium equation under polar coordinate system is established, and is linearized；Step S2:Under polar coordinate system, each element linear tide model of three phase power distribution networks is established；Step S3:According to power distribution network node power equilibrium equation after linearisation and each element linear tide model, linearisation power flow equation group is solved using LU factorization, obtains node voltage and phase angle to be asked.Polar coordinates three-phase distribution cable tidal current computing method provided by the present invention is adaptable, is suitable for active distribution network rapid Optimum and controls.
Description
Technical field
It is related to distribution power system load flow calculation field in electric system the present invention relates to bright, and in particular to one kind is applied to actively match
The linear tidal current computing method of three-phase polar coordinate system of power grid.
Background technology
Attention with people to ecological environment with the development of economy, regenerative resource clean electric power generation achieve significant hair
Exhibition.As distribution type renewable energy power generation is incorporated into power distribution network, high-adaptability, high robust trend towards active distribution network
Computational methods are urgently developed.
Conventional electrical distribution net power flow algorithm is divided into two classes, respectively fixed point iteration method and Newton-Laphson method.In the related technology,
Iteration calculating power system load flow is easy to be limited by convergence rate and reliability, therefore the poor practicability in terms of real time execution analysis.
The published method in part only considered the ZIP load models under conventional orthogonal coordinate system, and part discloses model and do not considered point
Influence etc. to distribution power system load flow calculation after cloth power supply is connected to the grid.
Invention content
In view of this, the purpose of the present invention is to provide one kind
To achieve the above object, the present invention adopts the following technical scheme that：
A kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network, it is characterised in that：Including with
Lower step：
Step S1：The power distribution network node power equilibrium equation under polar coordinate system is established, and is linearized；
Step S2：Under polar coordinate system, each element linear tide model of three phase power distribution networks is established；
Step S3：According to power distribution network node power equilibrium equation after linearisation and each element linear tide model, using LU
Decomposition method solves linearisation power flow equation group, obtains node voltage and phase angle to be asked.
Further, the element includes ZIP loads, three-phase and single-phase transformer, stepped voltage adjuster, distributed electrical
Source, distributed relaxation busbar.
Further, the step S1 is specially：
Step S11：Set linearization approximate formula as:
Wherein, θij=θi-θjIndicate the phase angle difference between two nodes of three-phase power distribution system, it is right according to disclosing knowledge
In distribution system Load flow calculation, θijIt is varied less compared with its initial value, i.e. θi-θj-(θij,0)≈0；sinθij' and cos θij' be respectively
sinθijWith cos θijLinear expression, the initial value of the element representation correlated variables of subscripting 0；
Step S12：Distribution system node voltage is U ≈ 1.0p.u., the amplitude and formula (1) of node voltage, (2) product
Linearly turn to：
U sinθij′≈(θi-θj-θij,0)cosθij,0+sinθij,0U (3)
U cosθij′≈cosθij,0U-(θi-θj-θij,0)sinθij,0 (4)
It is in the Taylor series of U=1.0p.u. neighborhoods, voltage magnitude inverse：1/U≈2-U；
Step S13:Assuming that there is n node in power grid, node active power balance equation is：
Wherein PiIt is injected for the active power of node, Pi=Pgi-Pdi, PgiThe generator active power connected by node,
PdiThe load active power connected by node；
Node reactive power is：
Wherein, QiIt is injected for the active power of node, Qi=Qgi-Qdi, QgiThe generator active power connected by node,
QdiThe load active power connected by node；I, j are node serial number, and U and θ indicate that voltage magnitude and phase angle, B and G divide respectively
Not Wei admittance matrix real and imaginary parts.
Further, the linear tide model of three phase power distribution networks ZIP loads is specially：
Consider that two kinds of connection types of Y types and Δ type carry out linear modelling to ZIP loads respectively；
1) the ZIP load uncertainty models of Y types connection are established：
It is in the Taylor series of U=1.0p.u. neighborhoods, voltage magnitude inverse：1/U ≈ 2-U, it can thus be concluded that node k connects
The active power of the Y connected loads connect injects equation：
Wherein, k is node serial number；WithFor known quantity, the active constant-impedance of load, constant current are indicated respectively
With invariable power part, three coefficients meetRelationship；Pk,φFor single-phase active power, Uk,φFor phase voltage；
The reactive power for the Y type connected loads that node k is connected injects equation：
In formula,WithFor known quantity, constant-impedance, constant current and the invariable power part of reactive load are indicated respectively,
Three coefficients meetRelationship；Qk,φFor single-phase reactive power, Uk,φFor phase voltage；
2) the ZIP load uncertainty models of Δ type connection are established：
By the differential seat angle along distribution line very close to initial differential seat angle, the mathematics for obtaining line voltage and phase voltage closes
System：
Wherein, φ 1, φ 2 indicate the phase in distribution system a/b/c three-phases, θφ1、θφ2Indicate phase angle；Point
Alternate complex voltage, single-phase complex voltage, θ are not indicatedφ10And θφ20It is distribution line relative to θφ1And θφ2Initial phase angle；
The single-phase active injection equation for the Δ connected load that node k is connected is represented by：
Wherein,Expression meets conditionZIP coefficients；
The single-phase idle injection equation of Δ type connected load that node k is connected is:
Relationship is as follows between each phase current of Δ type connected load and load access point phase current：
To the same complex number voltage for multiplying respective node at left and right sides of formula (12) equal sign, then with except respective node voltage width
Value, obtains：
Wherein, * indicates complex conjugate；
Formula (13) right branch electric current：
For the connection of Δ type
ZIP loads, power can be indicated with following equation：
Formula (10) and (11) are brought on the right side of formula (14), you can the linear equation for obtaining ZIP load injecting powers indicates
Form.
Further, the three-phase transformer is regarded as being made of three single-phase transformers；Establish single-phase transformer
Tide model is linearized, specially：
According to whether ground connection is divided into three kinds of wiring types, respectively Yg-Yg, Δ-Yg and Δ-Δ：
1) transformer winding ground connection Yg-Yg link models are established：
Branch current between the Yg-Yg connection primary sides node i of transformer winding, j is：
Wherein, t is the tap ratio of transformer winding.
To formula (15), linearization process branch complex power：
2) transformer winding Δ-Yg type link models are established：
Δ-Yg connection the primary sides of transformer winding, linearisation branch complex power are
By U cos θ in formula (3) and formula (4)ij' and U sin θsij' linearized expression substitutes into formula (17) and can be obtained branch
The lienarized equation of complex power；
For the complex power of node jIt can similarly obtain：
3) transformer winding Δ-Δ link model is established：
In primary side, linearisation branch complex power is：
Secondary side branch complex power linear model can still be indicated by formula (18), and the kl in formula is replaced i.e. with ij
It can.
Further, described to establish the linear tide model of stepped voltage adjuster, specially：Stepped voltage adjuster is built
Mould is small impedance transformer winding, is fixed as 10-9Perunit value, by centre-tapped transformer be divided into two single transformer windings into
Row analysis.
Further, described to establish the linear tide model of three phase power distribution networks distributed generation resource, specially：
To distributed generation resource Direct Modeling, the builtin voltage of balance is considered as variable, the distribution of PQ controls in tidal current analysis
Formula power supply equation is as follows：
Wherein, η1Psp+jη2QspIt is the injection complex power of internal node, η1To consider the active power effect of inverter losses
Rate, η2It indicates to consider the reactive power efficiency that inverter reactive power is lost；
Linearization process is carried out to nonlinear equation (20), is obtained：
The distributed generation resource of setting can control voltage, and power flow equation is converted to：
Wherein, UspIndicate that the specified voltage controling value of distributed generation resource, Re indicate real.
Further, described to establish the three phase power distribution networks relaxation linear tide model of busbar, specially：
Consider that injecting power total on each busbar of distributed generation resource, relaxation busbar active power injection equation are：
Wherein,It is initial value known to the total active power of distributed generation resource, γkIt is weighted for each generator and participates in system
Number, kgIt is calculative scalar, η1, k is the active power efficiency for the distributed generation resource k for considering inverter losses, ngIt is distribution
The quantity of formula power supply, a busbar may have a phase, two-phase or three-phase node.
1. a kind of linear Load flow calculation side of three-phase polar coordinate system applied to active distribution network according to claim 1
Method, it is characterised in that：The step S3 is specially：
Step S31:Linear trend is acquired by system of linear equations calculating, and system of linear equations is：
AX=b (25)
In formula (25), X is unknown variable, including node voltage amplitude and phase angle, and A is coefficient matrix, and b is the right；
Consider PQ nodes, ZIP loads, Yg-Yg type transformers linear power flow equation be：
Wherein,[a12
a13 a14]=[a32 a33 a34]=[Gijcosθij,0+Bijsinθij,0 -Gijsinθij,0+Bijcosθij,0 Gijsinθij,0-
Bijcosθij,0]；[a22 a23 a24]=[a42 a43 a44]=[- Bijcosθij,0+Gijsinθij,0 Bijsinθij,0+Gijcos
θij,0 -Gijcosθij,0-Bijsinθij,0]；
Step S32:Unknown variable in linear trend is the voltage magnitude and phase angle of each node, wherein for distribution wire
The contribution on road, the coefficient matrix to linearizing trend includes the right-hand side expression of formula (5) (6), for the ZIP of Y types, Δ type
Load to linearisation trend on the right of item contribution include formula (7), (8), (14) right-hand side expression, to distribution transformer, line
The contribution of property trend includes the expression formula of formula (16)-(19)；
Step S33:According to the linear tide model of each element of composition active distribution network, system of linear equations is ultimately formed
Coefficient matrices A and the right b, be then based on the LU decomposition techniques of matrix, acquire the numerical value of unknown variable X.
The present invention has the advantages that compared with prior art：
(1) present invention has fully considered ZIP loads and a series of three-phase equipment model, considers more comprehensive.Respectively
The connection of Y types and the connection of Δ type to ZIP loads and Yg-Yg, Δ-Yg and the three kinds of main wiring of Δ-Δ of transformer winding
Mode carries out linearization process, obtains the inearized model of each element.
(2) with the extensive access of distributed generation resource, the present invention overcomes three-phase linear trend under existing rectangular coordinate system
Model can not handle the shortcomings that voltage-controlled node in part and deficiency, fully consider influence of the voltage-controlled node to Load flow calculation.
(3) present invention has fully considered distribution in order to ensure three-phase linear trend acquired results are closer to actual conditions
The influence of relaxation bus networks model and distributed generation resource loss factor to active distribution network Load flow calculation.
Description of the drawings
Fig. 1 is flow diagram of the present invention；
Fig. 2 is step S2 sub-step schematic diagrames in one embodiment of the invention；
Fig. 3 is ZIP loads Δ type connection diagram of the present invention；
Fig. 4 is the transformer winding Yg-Yg type connection diagrams of the present invention；
Fig. 5 is the transformer winding Δ-Yg type connection diagrams of the present invention；
Fig. 6 is transformer winding Δ-Δ type connection diagram of the present invention；
Fig. 7 be the present invention impedance after three-phase distribution voltage source model schematic
In figure：A, b, c represent three-phase node,The connection of Δ type is represented per phase load electric current；I, j is primary
Side gusset, k, l are secondary side gusset, yikFor transformer impedance；ZabcFor distributed generation resource three-phase internal impedance,
Respectively distributed generation resource grid entry point three-phase voltage.
Specific implementation mode
The present invention will be further described with reference to the accompanying drawings and embodiments.
Fig. 1 is please referred to, the present invention provides a kind of linear tidal current computing method of three-phase polar coordinates applied to active distribution network,
Include the following steps：
Step S1：Polar coordinate system power distribution network node power equilibrium equation is established, and is linearized：
During establishing linearisation node power equation, following linearization approximate formula has been used：
Wherein, θij=θi-θjIndicate the phase angle difference between two nodes of three-phase power distribution system, it is right according to disclosing knowledge
In distribution system Load flow calculation, θijIt is varied less compared with its initial value, θi-θj-(θij,0)≈0；sinθij' and cos θij' it is sin respectively
θijWith cos θijLinear expression, the initial value of the element representation correlated variables of subscripting 0.
Distribution system node voltage meets U ≈ 1.0p.u., the linearisation of the amplitude and formula (1), (2) product of node voltage
For：
U sinθij′≈(θi-θj-θij,0)cosθij,0+sinθij,0U (3)
U cosθij′≈cosθij,0U-(θi-θj-θij,0)sinθij,0 (4)
It is in the Taylor series of U=1.0p.u. neighborhoods, voltage magnitude inverse：1/U≈2-U.
A busbar has three-phase in power distribution network, indicates three nodes, it is assumed that have n node, node active power in power grid
Equilibrium equation is：
Wherein PiIt is injected for the active power of node, Pi=Pgi-Pdi, PgiThe generator active power connected by node,
PdiThe load active power connected by node.
Similarly, node reactive power is：
Wherein QiIt is injected for the active power of node, Qi=Qgi-Qdi, QgiThe generator active power connected by node,
QdiThe load active power connected by node；I, j are node serial number, and U and θ indicate that voltage magnitude and phase angle, B and G divide respectively
Not Wei admittance matrix real and imaginary parts.
Step S2：Each element linear tide model of three phase power distribution networks, including ZIP loads, three are established under polar coordinate system
Phase and single-phase transformer, stepped voltage adjuster, distributed generation resource, distributed relaxation busbar；Detailed process is as follows：
Step S201：Consider that two kinds of connection types of Y types and Δ type carry out linear modelling to ZIP loads respectively.
1) the ZIP load uncertainty models of Y types connection are established：
It is in the Taylor series of U=1.0p.u. neighborhoods, voltage magnitude inverse：1/U ≈ 2-U, it can thus be concluded that node k connects
The active power of the Y connected loads connect injects equation：
Wherein, k is node serial number；WithFor known quantity, the active constant-impedance of load, constant current are indicated respectively
With invariable power part, three coefficients meetRelationship；Pk,φFor single-phase active power, Uk,φFor phase voltage.
It can similarly obtain, the reactive power injection equation for the Y type connected loads that node k is connected is：
In formula,WithFor known quantity, constant-impedance, constant current and the invariable power part of reactive load are indicated respectively,
Three coefficients meetRelationship；Qk,φFor single-phase reactive power, Uk,φFor phase voltage.
2) the ZIP load uncertainty models of Δ type connection are established：
Differential seat angle along distribution line is very close to initial differential seat angle, so line voltage and phase voltage have following mathematics
Relationship：
Wherein, φ 1, φ 2 indicate the phase in distribution system a/b/c three-phases, θφ1、θφ2Indicate phase angle；Point
Alternate complex voltage, single-phase complex voltage, θ are not indicatedφ10And θφ20It is distribution line relative to θφ1And θφ2Initial phase angle.
The single-phase active injection equation for the Δ connected load that node k is connected is represented by：
Wherein,Expression meets conditionZIP coefficients.
The single-phase idle injection equation of Δ type connected load that node k is connected, which can similarly be obtained, is:
As shown in figure 3, relationship is as follows between each phase current of Δ type connected load and load access point phase current：
To the same complex number voltage for multiplying respective node at left and right sides of formula (12) equal sign, then with except respective node voltage width
Value, obtains：
Wherein, * indicates complex conjugate.
Formula (13) right branch electric current
For the ZIP loads of Δ type connection, power can be indicated with following equation：
Formula (10) and (11) are brought on the right side of formula (14), you can the linear equation for obtaining ZIP load injecting powers indicates
Form.
Step S202：Establish distribution three-phase and single-phase transformer linearisation tide model.
In a power distribution system, three-phase transformer is regarded as being made of three single-phase transformers, and therefore, the present invention is directly built
The linearisation tide model of vertical single-phase transformer.According to whether ground connection, there are mainly three types of wiring type, respectively Yg-Yg, Δs-
Yg and Δ-Δ.
1) transformer winding ground connection Yg-Yg link models are established：
The Yg-Yg connections of transformer winding are as shown in Figure 4.Branch current between distribution system node i, j is：
Wherein, t is the tap ratio of transformer winding.
To formula (15), linearization process branch complex power：
2) transformer winding Δ-Yg type link models are established：
Δ-Yg the connections of transformer winding are as shown in Figure 5.In primary side, linearisation branch complex power is
By U cos θ in formula (3) and formula (4)ij' and U sin θsij' linearized expression substitutes into formula (17) and can be obtained branch
The lienarized equation of complex power.
For the complex power of node jIt can similarly obtain：
3) transformer winding Δ-Δ link model is established：
The Δ of transformer winding-Δ connection is as shown in Figure 6.In primary side, linearisation branch complex power is：
Secondary side branch complex power linear model can still be indicated by formula (18), and the kl in formula is replaced i.e. with ij
It can.
Step S203：Stepped voltage adjuster and centre-tapped transformer model：
Stepped voltage adjuster is modeled as small impedance transformer winding by the present invention, is fixed as 10-9 perunit values, the present invention
It is middle centre-tapped transformer is divided into two single transformer windings to analyze.
Step S204：Establish distributed generation resource linearisation tide model：
The present invention mainly discusses three-phase distributed generation resource.Because of distributed generation resource balanced configuration, three-phase is distributed after impedance
Formula voltage source model is as shown in Figure 7.
In order to which the builtin voltage to distributed generation resource Direct Modeling, balance is considered as variable in tidal current analysis, PQ controls
Distributed generation resource equation is as follows：
Wherein, η1Psp+jη2QspIt is the injection complex power of internal node, η1To consider the active power effect of inverter losses
Rate, η2It indicates to consider the reactive power efficiency that inverter reactive power is lost.
Linearization process is carried out to nonlinear equation (20), is obtained：
If the distributed generation resource modeled can control voltage, power flow equation is converted to：
Wherein, UspIndicate that the specified voltage controling value of distributed generation resource, Re indicate real.
Step S205：Establish distributed relaxation bus model：
Consider that injecting power total on each busbar of distributed generation resource, relaxation busbar active power injection equation are：
Wherein,It is initial value known to the total active power of distributed generation resource, γkIt is weighted for each generator and participates in system
Number, kgIt is calculative scalar, η1, k is the active power efficiency for the distributed generation resource k for considering inverter losses, and ng is distribution
The quantity of formula power supply, a busbar may have a phase, two-phase or three-phase node.
In order to ensure trend can solve, Reference Phase Angle needs to specify, and the Constraints of Equilibrium with reference to busbar is：
Wherein,It is the voltage magnitude with reference to busbar, is known quantity；θ0It is specified reference angle, is known quantity.
Step S3：Linearisation power flow equation group is solved using LU factorization, obtains node voltage to be asked, phase angle：
Linear trend is acquired by system of linear equations calculating, and system of linear equations is：
AX=b (25)
In formula (25), X is unknown variable, including node voltage amplitude and phase angle, and A is coefficient matrix, and b is the right.
Consider PQ nodes, ZIP loads, Yg-Yg type transformers linear power flow equation be：
Wherein,
[a12 a13 a14]=[a32 a33 a34]=[Gijcosθij,0+Bijsinθij,0 -Gijsinθij,0+Bijcosθij,0
Gijsinθij,0-Bijcosθij,0]；
[a22 a23 a24]=[a42 a43 a44]=[- Bijcosθij,0+Gijsinθij,0 Bijsinθij,0+Gijcosθij,0 -
Gijcosθij,0-Bijsinθij,0]；
Unknown variable in linear trend is the voltage magnitude and phase angle of each node.Wherein for distribution line, to line
The contribution of the coefficient matrix of property trend includes the right-hand side expression of formula (5) (6), for Y types, Δ type ZIP loads to line
Property trend on the right of item contribution include formula (7), (8), (14) right-hand side expression trend is linearized to distribution transformer
Contribution include formula (16)-(19) expression formula.Each element of traversal composition active distribution network, ultimately forms linear equation
The coefficient matrices A of group and the right b, are then based on the LU decomposition techniques of matrix, acquire the numerical value of unknown variable X.
The foregoing is merely presently preferred embodiments of the present invention, all equivalent changes done according to scope of the present invention patent with
Modification should all belong to the covering scope of the present invention.
Claims (9)
1. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network, it is characterised in that：Including following
Step：
Step S1：The power distribution network node power equilibrium equation under polar coordinate system is established, and is linearized；
Step S2:Under polar coordinate system, each element linear tide model of three phase power distribution networks is established；
Step S3:According to power distribution network node power equilibrium equation after linearisation and each element linear tide model, decomposed using LU
Method solves linearisation power flow equation group, obtains node voltage and phase angle to be asked.
2. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network according to claim 1,
It is characterized in that：The element includes ZIP loads, three-phase and single-phase transformer, stepped voltage adjuster, distributed generation resource, divides
Cloth relaxation busbar.
3. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network according to claim 1,
It is characterized in that：The step S1 is specially：
Step S11:Set linearization approximate formula as:
Wherein, θij=θi-θjIndicate the phase angle difference between two nodes of three-phase power distribution system, for distribution system Load flow calculation,
θijIt is varied less compared with its initial value, i.e. θi-θj-(θij,0)≈0；sinθ′ijWith cos θ 'ijIt is sin θ respectivelyijWith cos θijIt is linear
It indicates, the initial value of the element representation correlated variables of subscripting 0；
Step S12:Distribution system node voltage is U ≈ 1.0p.u., the amplitude and formula (1) of node voltage, (2) product it is linear
It turns to：
Usinθ′ij≈(θi-θj-θij,0)cosθij,0+sinθij,0U (3)
Ucosθ′ij≈cosθij,0U-(θi-θj-θij,0)sinθij,0 (4)
It is in the Taylor series of U=1.0p.u. neighborhoods, voltage magnitude inverse：1/U≈2-U；
Step S13:Assuming that there is n node in power grid, node active power balance equation is：
Wherein PiIt is injected for the active power of node, Pi=Pgi-Pdi, PgiThe generator active power connected by node, PdiFor
The load active power that node is connected；
Node reactive power is：
Wherein, QiIt is injected for the active power of node, Qi=Qgi-Qdi, QgiThe generator active power connected by node, QdiFor
The load active power that node is connected；I, j are node serial number, and U and θ indicate that voltage magnitude and phase angle, B and G are respectively respectively
The real and imaginary parts of admittance matrix.
4. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network according to claim 2,
It is characterized in that：The linear tide model of three phase power distribution networks ZIP loads is specially：
Consider that two kinds of connection types of Y types and Δ type carry out linear modelling to ZIP loads respectively；
1) the ZIP load uncertainty models of Y types connection are established：
It is in the Taylor series of U=1.0p.u. neighborhoods, voltage magnitude inverse：1/U ≈ 2-U, it can thus be concluded that the Y that node k is connected
The active power of connected load injects equation：
Wherein, k is node serial number；WithFor known quantity, the active constant-impedance of load, constant current and permanent work(are indicated respectively
Rate part, three coefficients meetRelationship；Pk,φFor single-phase active power, Uk,φFor phase voltage；
The reactive power for the Y type connected loads that node k is connected injects equation：
In formula,WithFor known quantity, constant-impedance, constant current and the invariable power part of reactive load are indicated respectively, three
Coefficient meetsRelationship；Qk,φFor single-phase reactive power, Uk,φFor phase voltage；
2) the ZIP load uncertainty models of Δ type connection are established：
By the differential seat angle along distribution line very close to initial differential seat angle, the mathematical relationship of line voltage and phase voltage is obtained：
Wherein, φ 1, φ 2 indicate the phase in distribution system a/b/c three-phases, θφ1、θφ2Indicate phase angle；Table respectively
Show alternate complex voltage, single-phase complex voltage, θφ10And θφ20It is distribution line relative to θφ1And θφ2Initial phase angle；
The single-phase active injection equation for the Δ connected load that node k is connected is represented by：
Wherein,Expression meets conditionZIP coefficients；
The single-phase idle injection equation of Δ type connected load that node k is connected is:
Relationship is as follows between each phase current of Δ type connected load and load access point phase current：
To, with the complex number voltage for multiplying respective node, then with respective node voltage amplitude is removed, being obtained at left and right sides of formula (12) equal sign：
Wherein, * indicates complex conjugate；
Formula (13) right branch electric current：
It is negative for the ZIP of Δ type connection
Lotus, power can be indicated with following equation：
Formula (10) and (11) are brought on the right side of formula (14), you can obtain the linear equation representation of ZIP load injecting powers.
5. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network according to claim 2,
It is characterized in that：The three-phase transformer is regarded as being made of three single-phase transformers；Establish the linearisation of single-phase transformer
Tide model, specially：
According to whether ground connection is divided into three kinds of wiring types, respectively Yg-Yg, Δ-Yg and Δ-Δ：
1) transformer winding ground connection Yg-Yg link models are established：
Branch current between the Yg-Yg connection primary sides node i of transformer winding, j is：
Wherein, t is the tap ratio of transformer winding.
To formula (15), linearization process branch complex power：
2) transformer winding Δ-Yg type link models are established：
Δ-Yg connection the primary sides of transformer winding, linearisation branch complex power are
By Ucos θ in formula (3) and formula (4)ij' and Usin θij' linearized expression substitutes into formula (17) and can be obtained branch complex power
Lienarized equation；
For the complex power of node jIt can similarly obtain：
3) transformer winding Δ-Δ link model is established：
In primary side, linearisation branch complex power is：
Secondary side branch complex power linear model can still be indicated by formula (18), and the kl in formula is replaced with ij.
6. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network according to claim 2,
It is characterized in that：It is described to establish the linear tide model of stepped voltage adjuster, specially：Stepped voltage adjuster is modeled as small
Impedance transformer winding, is fixed as 10-9Centre-tapped transformer is divided into two single transformer windings and is divided by perunit value
Analysis.
7. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network according to claim 2,
It is characterized in that：It is described to establish the linear tide model of three phase power distribution networks distributed generation resource, specially：
To distributed generation resource Direct Modeling, the builtin voltage of balance is considered as variable, the distributed electrical of PQ controls in tidal current analysis
Source equation is as follows：
Wherein, η1Psp+jη2QspIt is the injection complex power of internal node, η1To consider the active power efficiency of inverter losses, η2
It indicates to consider the reactive power efficiency that inverter reactive power is lost；
Linearization process is carried out to nonlinear equation (20), is obtained：
The distributed generation resource of setting can control voltage, and power flow equation is converted to：
Wherein, UspIndicate that the specified voltage controling value of distributed generation resource, Re indicate real.
8. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network according to claim 2,
It is characterized in that：It is described to establish the three phase power distribution networks relaxation linear tide model of busbar, specially：
Consider that injecting power total on each busbar of distributed generation resource, relaxation busbar active power injection equation are：
Wherein,It is initial value known to the total active power of distributed generation resource, γkIt is weighted for each generator and participates in coefficient, kg
It is calculative scalar, η1, k is the active power efficiency for the distributed generation resource k for considering inverter losses, ngIt is distributed electrical
The quantity in source, a busbar may have a phase, two-phase or three-phase node.
9. a kind of linear tidal current computing method of three-phase polar coordinate system applied to active distribution network according to claim 1,
It is characterized in that：The step S3 is specially：
Step S31：Linear trend is acquired by system of linear equations calculating, and system of linear equations is：
AX=b (25)
In formula (25), X is unknown variable, including node voltage amplitude and phase angle, and A is coefficient matrix, and b is the right；
Consider PQ nodes, ZIP loads, Yg-Yg type transformers linear power flow equation be：
Wherein,
[a12 a13 a14]=[a32 a33 a34]=[Gijcosθij,0+Bijsinθij,0 -Gijsinθij,0+Bijcosθij,0 Gijsin
θij,0-Bijcosθij,0]；
[a22 a23 a24]=[a42 a43 a44]=[- Bijcosθij,0+Gijsinθij,0 Bijsinθij,0+Gijcosθij,0 -
Gijcosθij,0-Bijsinθij,0]；
Step S32：Unknown variable in linear trend is the voltage magnitude and phase angle of each node, wherein for distribution line,
The contribution of coefficient matrix to linearizing trend includes the right-hand side expression of formula (5) (6), for the ZIP loads of Y types, Δ type
Contribution to item on the right of linearisation trend include formula (7), (8), (14) right-hand side expression, to distribution transformer, linearisation
The contribution of trend includes the expression formula of formula (16)-(19)；
Step S33：According to the linear tide model of each element of composition active distribution network, ultimately form system of linear equations is
Matrix number A and the right b, is then based on the LU decomposition techniques of matrix, acquires the numerical value of unknown variable X, obtain active distribution network
The voltage magnitude and phase angle of each node.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110518590A (en) * | 2019-08-05 | 2019-11-29 | 三峡大学 | Consider the linear tidal current computing method of power distribution network of static load characteristics |
| CN112231630A (en) * | 2020-10-26 | 2021-01-15 | 国家超级计算无锡中心 | Sparse matrix solving method based on FPGA parallel acceleration |
| CN113783211B (en) * | 2021-10-12 | 2023-10-31 | 国网福建省电力有限公司龙岩供电公司 | Power grid three-phase voltage unbalance analysis method based on three-phase tide technology |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008025162A1 (en) * | 2007-08-27 | 2008-03-06 | Sureshchandra Patel | System and method of loadflow calculation for electrical power system |
| CN104269872A (en) * | 2014-10-13 | 2015-01-07 | 国家电网公司 | Method for processing singularity of transformer three-phase node admittance matrix |
| CN106130025A (en) * | 2016-06-24 | 2016-11-16 | 西南石油大学 | A kind of linear method calculating three-phase distribution net trend based on loop analysis |
| CN106385035A (en) * | 2016-12-05 | 2017-02-08 | 国网江西省电力公司经济技术研究院 | DC power flow calculation method considering charging capacitance |
| CN106877337A (en) * | 2017-03-17 | 2017-06-20 | 南昌大学 | A kind of single-phase tidal current computing method of power distribution network based on linear load model |
| CN107069740A (en) * | 2017-03-17 | 2017-08-18 | 南昌大学 | A kind of power distribution network Three Phase Power Flow based on linear load model |
| CN107069741A (en) * | 2017-04-20 | 2017-08-18 | 河海大学 | A kind of novel linear tidal current computing method |
-
2018
- 2018-07-09 CN CN201810747029.4A patent/CN108718091B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008025162A1 (en) * | 2007-08-27 | 2008-03-06 | Sureshchandra Patel | System and method of loadflow calculation for electrical power system |
| CN104269872A (en) * | 2014-10-13 | 2015-01-07 | 国家电网公司 | Method for processing singularity of transformer three-phase node admittance matrix |
| CN106130025A (en) * | 2016-06-24 | 2016-11-16 | 西南石油大学 | A kind of linear method calculating three-phase distribution net trend based on loop analysis |
| CN106385035A (en) * | 2016-12-05 | 2017-02-08 | 国网江西省电力公司经济技术研究院 | DC power flow calculation method considering charging capacitance |
| CN106877337A (en) * | 2017-03-17 | 2017-06-20 | 南昌大学 | A kind of single-phase tidal current computing method of power distribution network based on linear load model |
| CN107069740A (en) * | 2017-03-17 | 2017-08-18 | 南昌大学 | A kind of power distribution network Three Phase Power Flow based on linear load model |
| CN107069741A (en) * | 2017-04-20 | 2017-08-18 | 河海大学 | A kind of novel linear tidal current computing method |
Non-Patent Citations (1)
| Title |
|---|
| SAIRAJ V. DHOPLE ET AL: "Linear Approximations to AC Power Flow in Rectangular Coordinates", 《2015 53RD ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON)》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110518590A (en) * | 2019-08-05 | 2019-11-29 | 三峡大学 | Consider the linear tidal current computing method of power distribution network of static load characteristics |
| CN110518590B (en) * | 2019-08-05 | 2022-12-20 | 三峡大学 | Power distribution network linear load flow calculation method considering load voltage static characteristics |
| CN112231630A (en) * | 2020-10-26 | 2021-01-15 | 国家超级计算无锡中心 | Sparse matrix solving method based on FPGA parallel acceleration |
| CN112231630B (en) * | 2020-10-26 | 2024-02-02 | 国家超级计算无锡中心 | Sparse matrix solving method based on FPGA parallel acceleration |
| CN113783211B (en) * | 2021-10-12 | 2023-10-31 | 国网福建省电力有限公司龙岩供电公司 | Power grid three-phase voltage unbalance analysis method based on three-phase tide technology |
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