CN108718091B - Three-phase polar coordinate system linear load flow calculation method applied to active power distribution network - Google Patents

Three-phase polar coordinate system linear load flow calculation method applied to active power distribution network Download PDF

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CN108718091B
CN108718091B CN201810747029.4A CN201810747029A CN108718091B CN 108718091 B CN108718091 B CN 108718091B CN 201810747029 A CN201810747029 A CN 201810747029A CN 108718091 B CN108718091 B CN 108718091B
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node
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CN108718091A (en
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林毅
巨云涛
林章岁
张永华
方朝雄
葛夫超
邱柳青
唐雨晨
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China Agricultural University
State Grid Fujian Electric Power Co Ltd
Economic and Technological Research Institute of State Grid Fujian Electric Power Co Ltd
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China Agricultural University
State Grid Fujian Electric Power Co Ltd
Economic and Technological Research Institute of State Grid Fujian Electric Power Co Ltd
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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
    • 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
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Abstract

The invention relates to a three-phase polar coordinate system linear load flow calculation method applied to an active power distribution network, which comprises the following steps: step S1: establishing a power balance equation of the power distribution network node under a polar coordinate system, and performing linearization; step S2, establishing a linear power flow model of each element of the three-phase power distribution network in a polar coordinate system; and step S3, solving the linearized power flow equation set by adopting an LU decomposition method according to the linearized power distribution network node power balance equation and the linearized power flow model of each element, and acquiring the node voltage and the phase angle to be solved. The polar coordinate three-phase power distribution network linear load flow calculation method provided by the invention has strong adaptability and is suitable for rapid optimization control of the active power distribution network.

Description

Three-phase polar coordinate system linear load flow calculation method applied to active power distribution network
Technical Field
The invention relates to the field of power distribution network load flow calculation in a power system, in particular to a three-phase polar coordinate system linear load flow calculation method applied to an active power distribution network.
Background
With the development of economy and the attention of people on ecological environment, the clean power generation of renewable energy sources has made remarkable development. With the integration of distributed renewable energy power generation into a power distribution network, a high-adaptability and high-robustness load flow calculation method for an active power distribution network is in urgent need of development.
Traditional power distribution network power flow algorithms are divided into two types, namely a fixed point iteration method and a Newton Raphson method. In the related art, the iterative power flow calculation method is easily limited by convergence speed and reliability, and therefore, the method is poor in practicability in real-time operation analysis. Part of the disclosed methods only consider a ZIP load model under a traditional rectangular coordinate system, and part of the disclosed models do not consider the influence of the distributed power supply on power flow calculation of the power distribution network after the distributed power supply is merged into the power grid.
Disclosure of Invention
In view of the above, the present invention is to provide a method for producing
In order to achieve the purpose, the invention adopts the following technical scheme:
a three-phase polar coordinate system linear load flow calculation method applied to an active power distribution network is characterized by comprising the following steps: the method comprises the following steps:
step S1: establishing a power balance equation of the power distribution network node under a polar coordinate system, and performing linearization;
step S2: establishing a linear power flow model of each element of the three-phase power distribution network under a polar coordinate system;
step S3: and solving the linearized power flow equation set by adopting an LU decomposition method according to the linearized power distribution network node power balance equation and the linearized power flow model of each element to obtain the node voltage and the phase angle to be solved.
Further, the components include ZIP loads, three-phase and single-phase transformers, step voltage regulators, distributed power supplies, distributed slack buses.
Further, the step S1 is specifically:
step S11: the linearized approximation formula is set as:
Figure BDA0001724614280000021
Figure BDA0001724614280000022
wherein, thetaij＝θi-θjRepresenting the phase angle difference between two nodes of a three-phase distribution system, and calculating the power flow of the distribution system according to the published knowledgeijLess variation than its initial value, i.e. thetai-θj-(θij,0)≈0；sinθij' and cos θij' is sin θ respectivelyijAnd cos θijThe linear representation of (a), the element with subscript 0 represents the initial value of the relevant variable;
step S12: the node voltage of the power distribution system is U ≈ 1.0p.u., and the amplitude of the node voltage and the linearization of the product of the equation (1) and the equation (2) are as follows:
U sinθij′≈(θi-θj-θij,0)cosθij,0+sinθij,0U (3)
U cosθij′≈cosθij,0U-(θi-θj-θij,0)sinθij,0 (4)
in the neighborhood of U ═ 1.0p.u., the taylor series of the inverse of the voltage amplitude is: 1/U is approximately equal to 2-U;
and step S13, assuming that n nodes exist in the power grid, the active power balance equation of the nodes is as follows:
Figure BDA0001724614280000031
wherein P isiFor active power injection of the node, Pi＝Pgi-Pdi，PgiActive power of generator connected to node, PdiLoad active power connected for the node;
the reactive power of the node is as follows:
Figure BDA0001724614280000032
wherein Q isiFor active power injection of the node, Qi＝Qgi-Qdi，QgiActive power of generator connected to node, QdiLoad active power connected for the node; i, j are node numbers, U and theta respectively represent voltage amplitude and phase angle, and B and G are respectively real parts and imaginary parts of the admittance matrix.
Further, the three-phase distribution network ZIP load linear power flow model specifically includes:
linear modeling is carried out on the ZIP load by respectively considering two connection modes of a Y type and a delta type;
1) establishing a ZIP load flow model of Y-shaped connection:
in the neighborhood of U ═ 1.0p.u., the taylor series of the inverse of the voltage amplitude is: 1/U is approximately equal to 2-U, so that the active power injection equation of the Y connection load connected with the node k is obtained as follows:
Figure BDA0001724614280000041
wherein k is a node number;
Figure BDA0001724614280000042
and
Figure BDA0001724614280000043
the constant impedance, the constant current and the constant power part of the load with work are respectively expressed by known quantities, and three coefficients satisfy
Figure BDA0001724614280000044
The relationship of (1); pk,φIs single-phase active power, Uk,φIs a phase voltage;
the reactive power injection equation of the Y-shaped connection load connected with the node k is as follows:
Figure BDA0001724614280000045
in the formula,
Figure BDA0001724614280000046
and
Figure BDA0001724614280000047
the constant impedance, the constant current and the constant power part of the load reactive power are respectively expressed as known quantities, and three coefficients satisfy
Figure BDA0001724614280000048
The relationship of (1); qk,φFor single-phase reactive power, Uk,φIs a phase voltage;
2) establishing a ZIP load flow model of delta connection:
from the angular difference along the distribution line very close to the initial angular difference, the mathematical relationship between line voltage and phase voltage is obtained:
Figure BDA0001724614280000049
wherein, phi 1 and phi 2 represent one phase of a/b/c three phases of the power distribution system, and thetaφ1、θφ2Represents a phase angle;
Figure BDA00017246142800000410
respectively representing phase-to-phase complex voltage, single-phase complex voltage, thetaφ10And thetaφ20Is a distribution line relative to thetaφ1And thetaφ2The initial phase angle of (a);
the single-phase active injection equation for the delta connection load to which node k is connected can be expressed as:
Figure BDA0001724614280000051
wherein,
Figure BDA0001724614280000052
indicates that the condition is satisfied
Figure BDA0001724614280000053
ZIP coefficient of (D);
the delta-type connection load single-phase reactive injection equation connected with the node k is as follows:
Figure BDA0001724614280000054
the relationship between the delta connection load phase current and the load access point phase current is as follows:
Figure BDA0001724614280000055
multiplying the left side and the right side of the equation (12) with the same sign by the complex voltage of each node, and then dividing the voltage amplitude of each node to obtain:
Figure BDA0001724614280000056
wherein denotes a complex conjugate;
equation (13) right branch current:
Figure BDA0001724614280000057
for delta-connected ZIP loads, the power can be expressed by the following equation:
Figure BDA0001724614280000061
substituting equations (10) and (11) to the right of equation (14) yields a linear equation representation of the ZIP load injection power.
Further, the three-phase transformer may be considered to be composed of three single-phase transformers; establishing a linearization tide model of the single-phase transformer, specifically:
three types of connections, Yg-Yg, Δ -Yg and Δ - Δ, are classified according to whether grounding is performed:
1) establishing a transformer winding grounding Yg-Yg connection model:
the branch current between the Yg-Yg connection primary side nodes i and j of the transformer winding is as follows:
Figure BDA0001724614280000062
wherein t is the tapping ratio of the transformer winding.
For equation (15), the branch complex power is linearized:
Figure BDA0001724614280000063
2) establishing a delta-Yg type connection model of the transformer winding:
the delta-Yg of the transformer winding is connected with the primary side, and the complex power of the linear branch is
Figure BDA0001724614280000071
The general formula (3) and the general formula (4) are expressed in terms of U cos thetaij' and U sin θijThe linear expression is substituted for the formula (17) to obtain a linear equation of branch complex power;
complex power for node j
Figure BDA0001724614280000072
The same can be obtained:
Figure BDA0001724614280000073
3) establishing a delta-delta connection model of a transformer winding:
on the primary side, the complex power of the linearization branch is:
Figure BDA0001724614280000074
the secondary side branch complex power linear model can still be represented by formula (18), and kl in the formula can be replaced by ij.
Further, the establishing of the linear power flow model of the step voltage regulator specifically includes: modeling the step voltage regulator as a low impedance transformer winding, fixed at 10-9Per unit value, the center tapped transformer is divided into two single transformer windings for analysis.
Further, the establishing of the linear power flow model of the three-phase distribution network distributed power supply specifically includes:
directly modeling the distributed power supply, wherein the balanced internal voltage is regarded as a variable in power flow analysis, and a distributed power supply equation controlled by PQ is as follows:
Figure BDA0001724614280000081
wherein eta is1Psp+jη2QspIs the injected complex power of the internal node, eta1Active power efficiency, η, to account for inverter losses2Representing a reactive power efficiency taking into account the reactive power losses of the inverter;
the nonlinear equation (20) is linearized to obtain:
Figure BDA0001724614280000082
the set distributed power supply can control voltage, and the power flow equation is converted into:
Figure BDA0001724614280000083
wherein, UspIndicates a voltage control value designated by the distributed power source, and Re indicatesThe real part of the complex number.
Further, the establishing of the three-phase distribution network slack bus linear power flow model specifically includes:
considering the total injected power on each bus of the distributed power supply, the relaxed bus active power injection equation is:
Figure BDA0001724614280000091
wherein,
Figure BDA0001724614280000092
is a known initial value of the total active power of the distributed power supply, gammakWeighting the participation coefficient, k, for each generatorgIs a scalar quantity, η, to be calculated1K is the active power efficiency of the distributed power supply k taking into account the inverter losses, ngFor the number of distributed power sources, a bus may have one, two or three phase nodes.
1. The method for calculating the linear power flow of the three-phase polar coordinate system applied to the active power distribution network according to claim 1, wherein: the step S3 specifically includes:
and step S31, calculating the linear power flow through a linear equation set, wherein the linear equation set is as follows:
AX＝b (25)
in the formula (25), X is a variable to be solved and comprises a node voltage amplitude and a phase angle, A is a coefficient matrix, and b is a right term;
considering the PQ node, the ZIP load and the linear power flow equation of the Yg-Yg type transformer as follows:
Figure BDA0001724614280000093
wherein,
Figure BDA0001724614280000094
[a12a13 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]；
Figure BDA0001724614280000101
Figure BDA0001724614280000102
step S32, the variables to be solved in the linear power flow are the voltage amplitude and the phase angle of each node, wherein for the distribution line, the contribution of the variables to the coefficient matrix of the linear power flow comprises the right expression of the formulas (5) and (6), the contribution of the ZIP loads of the Y type and the delta type to the right term of the linear power flow comprises the right expression of the formulas (7), (8) and (14), and the contribution of the linear power flow comprises the expressions of the formulas (16) to (19) for the distribution transformer;
and S33, finally forming a coefficient matrix A and a right term b of the linear equation set according to the linear power flow model of each element forming the active power distribution network, and then solving the numerical value of the variable X to be solved based on the LU decomposition technology of the matrix.
Compared with the prior art, the invention has the following beneficial effects:
(1) according to the invention, ZIP load and a series of three-phase equipment models are fully considered, so that the consideration is more comprehensive. And respectively carrying out linearization processing on the Y-type connection and the delta-type connection of the ZIP load and three main wiring modes of Yg-Yg, delta-Yg and delta-delta of the transformer winding to obtain a linearization model of each element.
(2) With the wide access of the distributed power supply, the method overcomes the defect and the defect that the three-phase linearized power flow model under the existing rectangular coordinate system cannot process the local voltage control node, and fully considers the influence of the voltage control node on the power flow calculation.
(3) In order to ensure that the obtained result of the three-phase linear power flow is closer to the actual condition, the influence of a distributed loose bus network model and a distributed power supply loss factor on the power flow calculation of the active power distribution network is fully considered.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a diagram illustrating the substep of step S2 according to an embodiment of the present invention;
FIG. 3 is a ZIP load delta connection schematic of the present invention;
FIG. 4 is a Yg-Yg type connection schematic of the transformer winding of the present invention;
FIG. 5 is a schematic diagram of a delta-Yg type connection for a transformer winding according to the present invention;
FIG. 6 is a delta-delta connection schematic of the transformer winding of the present invention;
FIG. 7 is a schematic diagram of a post-impedance three-phase distributed voltage source model of the present invention
In the figure: a. b and c represent three-phase nodes,
Figure BDA0001724614280000111
representing delta type connection load current of each phase; i. j is a primary side node, k, l are secondary side nodes, yikIs the transformer impedance; zabcIs the three-phase internal impedance of the distributed power supply,
Figure BDA0001724614280000112
and the three-phase voltages are distributed power supply grid-connected points respectively.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 1, the present invention provides a three-phase polar linear power flow calculation method applied to an active power distribution network, including the following steps:
step S1: establishing a power balance equation of a power distribution network node in a polar coordinate system, and linearizing:
in establishing the linearized node power equation, the following linearized approximation formula is used:
Figure BDA0001724614280000121
Figure BDA0001724614280000122
wherein, thetaij＝θi-θjRepresenting the phase angle difference between two nodes of a three-phase distribution system, and calculating the power flow of the distribution system according to the published knowledgeijIs less changed than its initial value, thetai-θj-(θij,0)≈0；sinθij' and cos θij' is sin θ respectivelyijAnd cos θijThe linear representation of (a) with the subscript 0 represents the initial value of the relevant variable.
The node voltage of the power distribution system meets the condition that U is approximately equal to 1.0p.u., and the amplitude of the node voltage and the linearization of the product of the equations (1) and (2) are as follows:
U sinθij′≈(θi-θj-θij,0)cosθij,0+sinθij,0U (3)
U cosθij′≈cosθij,0U-(θi-θj-θij,0)sinθij,0 (4)
in the neighborhood of U ═ 1.0p.u., the taylor series of the inverse of the voltage amplitude is: 1/U is approximately equal to 2-U.
A bus in the power distribution network has three phases, three nodes are represented, if n nodes exist in the power distribution network, an active power balance equation of the nodes is as follows:
Figure BDA0001724614280000131
wherein P isiFor active power injection of the node, Pi＝Pgi-Pdi，PgiActive power of generator connected to node, PdiThe active power of the load connected to the node.
Similarly, the node reactive power is:
Figure BDA0001724614280000132
wherein QiFor active power injection of the node, Qi＝Qgi-Qdi，QgiActive power of generator connected to node, QdiLoad active power connected for the node; i, j are node numbers, U and theta respectively represent voltage amplitude and phase angle, and B and G are respectively real parts and imaginary parts of the admittance matrix.
Step S2: establishing a linear power flow model of each element of the three-phase power distribution network under a polar coordinate system, wherein the linear power flow model comprises a ZIP load, three-phase and single-phase transformers, a stepping voltage regulator, a distributed power supply and a distributed relaxation bus; the specific process is as follows:
step S201: and linear modeling is carried out on the ZIP load by respectively considering two connection modes of a Y type and a delta type.
1) Establishing a ZIP load flow model of Y-shaped connection:
in the neighborhood of U ═ 1.0p.u., the taylor series of the inverse of the voltage amplitude is: 1/U is approximately equal to 2-U, so that the active power injection equation of the Y connection load connected with the node k is obtained as follows:
Figure BDA0001724614280000141
wherein k is a node number;
Figure BDA0001724614280000142
and
Figure BDA0001724614280000143
the constant impedance, the constant current and the constant power part of the load with work are respectively expressed by known quantities, and three coefficients satisfy
Figure BDA0001724614280000144
The relationship of (1); pk,φIs single-phase active power, Uk,φIs the phase voltage.
In the same way, the reactive power injection equation of the Y-type connection load connected to the node k is:
Figure BDA0001724614280000145
in the formula,
Figure BDA0001724614280000146
and
Figure BDA0001724614280000147
the constant impedance, the constant current and the constant power part of the load reactive power are respectively expressed as known quantities, and three coefficients satisfy
Figure BDA0001724614280000148
The relationship of (1); qk,φFor single-phase reactive power, Uk,φIs the phase voltage.
2) Establishing a ZIP load flow model of delta connection:
the angle difference along the distribution line is very close to the initial angle difference, so the line voltage and the phase voltage have the following mathematical relationship:
Figure BDA0001724614280000149
wherein, phi 1 and phi 2 represent one phase of a/b/c three phases of the power distribution system, and thetaφ1、θφ2Represents a phase angle;
Figure BDA0001724614280000151
respectively representing phase-to-phase complex voltage, single-phase complex voltage, thetaφ10And thetaφ20Is a distribution line relative to thetaφ1And thetaφ2The initial phase angle of (c).
The single-phase active injection equation for the delta connection load to which node k is connected can be expressed as:
Figure BDA0001724614280000152
wherein,
Figure BDA0001724614280000153
indicates that the condition is satisfied
Figure BDA0001724614280000154
ZIP coefficient of (1).
In the same way, the equation of the delta-type connection load single-phase reactive injection connected with the node k is as follows:
Figure BDA0001724614280000155
as shown in fig. 3, the relationship between the delta connection load phase current and the load access point phase current is as follows:
Figure BDA0001724614280000156
multiplying the left side and the right side of the equation (12) with the same sign by the complex voltage of each node, and then dividing the voltage amplitude of each node to obtain:
Figure BDA0001724614280000161
wherein denotes a complex conjugate.
Right branch current of formula (13)
Figure BDA0001724614280000162
For delta-connected ZIP loads, the power can be expressed by the following equation:
Figure BDA0001724614280000163
substituting equations (10) and (11) to the right of equation (14) yields a linear equation representation of the ZIP load injection power.
Step S202: and establishing a linear power flow model of the three-phase and single-phase power distribution transformer.
In a power distribution system, a three-phase transformer can be considered to be composed of three single-phase transformers, so that the invention directly establishes a linearized power flow model of the single-phase transformers. There are three main types of connections, Yg-Yg, Δ -Yg and Δ - Δ, depending on whether grounding is provided or not.
1) Establishing a transformer winding grounding Yg-Yg connection model:
the Yg-Yg connections of the transformer windings are shown in fig. 4. The branch current between the nodes i and j of the power distribution system is as follows:
Figure BDA0001724614280000164
wherein t is the tapping ratio of the transformer winding.
For equation (15), the branch complex power is linearized:
Figure BDA0001724614280000171
2) establishing a delta-Yg type connection model of the transformer winding:
the delta-Yg connections for the transformer windings are shown in fig. 5. On the primary side, the complex power of the linearization branch is
Figure BDA0001724614280000172
The general formula (3) and the general formula (4) are expressed in terms of U cos thetaij' and U sin θijThe linear expression is substituted for the formula (17) to obtain a linear equation of branch complex power.
Complex power for node j
Figure BDA0001724614280000173
The same can be obtained:
Figure BDA0001724614280000174
3) establishing a delta-delta connection model of a transformer winding:
the delta-delta connections for the transformer windings are shown in figure 6. On the primary side, the complex power of the linearization branch is:
Figure BDA0001724614280000181
the secondary side branch complex power linear model can still be represented by formula (18), and kl in the formula can be replaced by ij.
Step S203: step voltage regulator and center tapped transformer model:
the step voltage regulator is modeled into a small-impedance transformer winding, the small-impedance transformer winding is fixed to be a per unit value of 10-9, and a center-tapped transformer is divided into two single transformer windings for analysis.
Step S204: establishing a distributed power supply linearization power flow model:
the present invention is primarily discussed in relation to three-phase distributed power supplies. Because the distributed power supplies are symmetrically configured, the impedance post-three-phase distributed voltage source model is shown in fig. 7.
In order to directly model the distributed power supply, the balanced internal voltage is regarded as a variable in the power flow analysis, and the distributed power supply equation of PQ control is as follows:
Figure BDA0001724614280000182
wherein eta is1Psp+jη2QspIs the injected complex power of the internal node, eta1Active power efficiency, η, to account for inverter losses2Representing reactive power efficiency taking into account the inverter reactive power losses.
The nonlinear equation (20) is linearized to obtain:
Figure BDA0001724614280000191
if the modeled distributed power supply is capable of controlling voltage, the power flow equation is converted to:
Figure BDA0001724614280000192
wherein, UspDenotes a voltage control value designated by the distributed power source, and Re denotes a real part of the complex number.
Step S205: establishing a distributed loose bus model:
considering the total injected power on each bus of the distributed power supply, the relaxed bus active power injection equation is:
Figure BDA0001724614280000193
wherein,
Figure BDA0001724614280000194
is a known initial value of the total active power of the distributed power supply, gammakWeighting the participation coefficient, k, for each generatorgIs a scalar quantity, η, to be calculated1Where k is the active power efficiency of the distributed power supply k considering inverter losses and ng is the number of distributed power supplies, a bus may have one, two or three phase nodes.
To ensure that the power flow can be solved, a reference phase angle needs to be specified, and the balance constraint of the reference bus is:
Figure BDA0001724614280000195
wherein,
Figure BDA0001724614280000201
is the voltage amplitude of the reference bus, which is a known quantity; theta0Is a specified reference angle, a known quantity.
Step S3: solving a linearized power flow equation set by adopting an LU decomposition method to obtain node voltage and phase angle to be solved:
the linear power flow is calculated by a linear equation set, wherein the linear equation set is as follows:
AX＝b (25)
in equation (25), X is the variable to be solved, including the node voltage amplitude and phase angle, a is the coefficient matrix, and b is the right term.
Considering the PQ node, the ZIP load and the linear power flow equation of the Yg-Yg type transformer as follows:
Figure BDA0001724614280000202
wherein,
Figure BDA0001724614280000203
[a12 a13 a14]＝[a32 a33 a34]＝[Gijcosθij,0+Bijsinθij,0 -Gijsinθij,0+Bijcosθij,0Gijsinθij,0-Bijcosθij,0]；
[a22 a23 a24]＝[a42 a43 a44]＝[-Bijcosθij,0+Gijsinθij,0 Bijsinθij,0+Gijcosθij,0 -Gijcosθij,0-Bijsinθij,0]；
Figure BDA0001724614280000204
Figure BDA0001724614280000211
the variables to be solved in the linear power flow are the voltage amplitude and the phase angle of each node. Wherein for the distribution line, the contribution of the distribution line to the coefficient matrix of the linearized power flow comprises the right expression of the formulas (5) and (6), the contribution of the Y-type and delta-type ZIP loads to the right term of the linearized power flow comprises the right expression of the formulas (7), (8) and (14), and the contribution of the linearized power flow comprises the expressions of the formulas (16) to (19) for the distribution transformer. And traversing each element forming the active power distribution network, finally forming a coefficient matrix A and a right term b of the linear equation set, and then solving the numerical value of the variable X to be solved based on the LU decomposition technology of the matrix.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (8)

1. A three-phase polar coordinate system linear load flow calculation method applied to an active power distribution network is characterized by comprising the following steps: the method comprises the following steps:
step S1: establishing a power balance equation of the power distribution network node under a polar coordinate system, and performing linearization;
step S2, establishing a linear power flow model of each element of the three-phase power distribution network in a polar coordinate system;
step S3, solving a linearized power flow equation set by adopting an LU decomposition method according to the linearized power distribution network node power balance equation and the linearized power flow model of each element to obtain node voltage and phase angle to be solved;
the step S1 specifically includes:
step S11, setting the linear approximate formula as:
Figure FDA0003151905610000011
Figure FDA0003151905610000012
wherein, thetaij＝θi-θjRepresenting the phase angle difference between two nodes of a three-phase distribution system, theta, for a power distribution system load flow calculationijLess variation than its initial value, i.e. thetai-θj-(θij,0)≈0；sinθ′ijAnd cos θ'ijAre each sin θijAnd cos θijThe linear representation of (a), the element with subscript 0 represents the initial value of the relevant variable;
and step S12, the node voltage of the power distribution system is U ≈ 1.0p.u., and the amplitude of the node voltage and the linearization of the product of the expression (1) and the expression (2) are as follows:
Usinθ′ij≈(θi-θj-θij,0)cosθij,0+sinθij,0U (3)
Ucosθ′ij≈cosθij,0U-(θi-θj-θij,0)sinθij,0 (4)
in the neighborhood of U ═ 1.0p.u., the taylor series of the inverse of the voltage amplitude is: 1/U is approximately equal to 2-U;
step S13, assuming that there are n nodes in the power grid, the active power balance equation of the nodes is
Figure FDA0003151905610000021
Wherein P isiFor active power injection of the node, Pi＝Pgi-Pdi，PgiActive power of generator connected to node, PdiLoad active power connected for the node;
the reactive power of the node is as follows:
Figure FDA0003151905610000022
wherein Q isiFor reactive power injection of nodes, Qi＝Qgi-Qdi，QgiActive power of generator connected to node, QdiLoad active power connected for the node; i, j are node numbers, U and theta respectively represent voltage amplitude and phase angle, and B and G are respectively real parts and imaginary parts of the admittance matrix.
2. The method for calculating the linear power flow of the three-phase polar coordinate system applied to the active power distribution network according to claim 1, wherein: the components include ZIP loads, three-phase and single-phase transformers, step voltage regulators, distributed power supplies, distributed relaxation buses.
3. The method for calculating the linear power flow of the three-phase polar coordinate system applied to the active power distribution network according to claim 2, wherein: the three-phase power distribution network ZIP load linear power flow model specifically comprises the following steps:
linear modeling is carried out on the ZIP load by respectively considering two connection modes of a Y type and a delta type;
1) establishing a ZIP load flow model of Y-shaped connection:
in the neighborhood of U ═ 1.0p.u., the taylor series of the inverse of the voltage amplitude is: 1/U is approximately equal to 2-U, so that the active power injection equation of the Y connection load connected with the node k can be obtained as
Figure FDA0003151905610000031
Wherein k is a node number;
Figure FDA0003151905610000032
and
Figure FDA0003151905610000033
the constant impedance, the constant current and the constant power part of the load with work are respectively expressed by known quantities, and three coefficients satisfy
Figure FDA0003151905610000034
The relationship of (1); pk,φIs single-phase active power, Uk,φIs a phase voltage;
the reactive power injection equation of the Y-shaped connection load connected with the node k is as follows:
Figure FDA0003151905610000035
in the formula,
Figure FDA0003151905610000036
and
Figure FDA0003151905610000037
the constant impedance, the constant current and the constant power part of the load reactive power are respectively expressed as known quantities, and three coefficients satisfy
Figure FDA0003151905610000038
The relationship of (1); qk,φFor single-phase reactive power, Uk,φIs a phase voltage;
2) establishing a ZIP load flow model of delta connection:
from the angular difference along the distribution line approaching the initial angular difference, a mathematical relationship between line voltage and phase voltage is obtained:
Figure FDA0003151905610000041
wherein, phi 1 and phi 2 represent one phase of a/b/c three phases of the power distribution system, and thetaφ1、θφ2Represents a phase angle;
Figure FDA0003151905610000042
respectively representing phase-to-phase complex voltage, single-phase complex voltage, thetaφ10And thetaφ20Is a distribution line relative to thetaφ1And thetaφ2The initial phase angle of (a);
the single-phase active injection equation for the delta connection load to which node k is connected can be expressed as:
Figure FDA0003151905610000043
wherein,
Figure FDA0003151905610000044
indicates that the condition is satisfied
Figure FDA0003151905610000045
ZIP coefficient of (D);
the delta-type connection load single-phase reactive injection equation connected with the node k is as follows:
Figure FDA0003151905610000046
the relationship between the delta connection load phase current and the load access point phase current is as follows:
Figure FDA0003151905610000051
Figure FDA0003151905610000052
Figure FDA0003151905610000053
multiplying the left side and the right side of the equation (12) with the same sign by the complex voltage of each node, and then dividing the voltage amplitude of each node to obtain:
Figure FDA0003151905610000054
Figure FDA0003151905610000055
Figure FDA0003151905610000056
wherein denotes a complex conjugate;
equation (13) right branch current:
Figure FDA0003151905610000057
for delta-connected ZIP loads, the power can be expressed by the following equation:
Figure FDA0003151905610000058
Figure FDA0003151905610000059
Figure FDA00031519056100000510
substituting equations (10) and (11) to the right of equation (14) yields a linear equation representation of the ZIP load injection power.
4. The method for calculating the linear power flow of the three-phase polar coordinate system applied to the active power distribution network according to claim 2, wherein: the three-phase transformer can be considered to be composed of three single-phase transformers; establishing a linearization tide model of the single-phase transformer, specifically:
three types of connections, Yg-Yg, Δ -Yg and Δ - Δ, are classified according to whether grounding is performed:
1) establishing a transformer winding grounding Yg-Yg connection model:
the branch current between the Yg-Yg connection primary side nodes i and j of the transformer winding is as follows:
Figure FDA00031519056100000511
wherein t is the tapping ratio of the transformer winding;
for equation (15), the branch complex power is linearized:
Figure FDA0003151905610000061
2) establishing a delta-Yg type connection model of the transformer winding:
the delta-Yg of the transformer winding is connected with the primary side, and the complex power of the linear branch is
Figure FDA0003151905610000062
Providing Ucos theta 'in the formula (3) and the formula (4)'ijAnd Usin θ'ijThe linear expression is substituted for the formula (17) to obtain a linear equation of branch complex power;
complex power for node j
Figure FDA0003151905610000063
The same can be obtained:
Figure FDA0003151905610000071
3) establishing a delta-delta connection model of a transformer winding:
on the primary side, the complex power of the linearization branch is:
Figure FDA0003151905610000072
the secondary side branch complex power linear model can still be represented by formula (18), and kl in the formula can be replaced by ij.
5. The method for calculating the linear power flow of the three-phase polar coordinate system applied to the active power distribution network according to claim 2, wherein: the step voltage regulator linear power flow model is established by the following steps: modeling the step voltage regulator as a low impedance transformer winding, fixed at 10-9Per unit value, the center tapped transformer is divided into two single transformer windings for analysis.
6. The method for calculating the linear power flow of the three-phase polar coordinate system applied to the active power distribution network according to claim 2, wherein: the establishment of the three-phase distribution network distributed power supply linear power flow model specifically comprises the following steps:
directly modeling the distributed power supply, wherein the balanced internal voltage is regarded as a variable in power flow analysis, and a distributed power supply equation controlled by PQ is as follows:
Figure FDA0003151905610000081
wherein eta is1Psp+jη2QspIs the injected complex power of the internal node, eta1Active power efficiency, η, to account for inverter losses2Representing a reactive power efficiency taking into account the reactive power losses of the inverter;
the nonlinear equation (20) is linearized to obtain:
Figure FDA0003151905610000082
the set distributed power supply can control voltage, and the power flow equation is converted into:
Figure FDA0003151905610000083
wherein, UspDenotes a voltage control value designated by the distributed power source, and Re denotes a real part of the complex number.
7. The method for calculating the linear power flow of the three-phase polar coordinate system applied to the active power distribution network according to claim 2, wherein: the method for establishing the three-phase distribution network slack bus linear power flow model specifically comprises the following steps:
considering the total injected power on each bus of the distributed power supply, the relaxed bus active power injection equation is:
Figure FDA0003151905610000084
wherein,
Figure FDA0003151905610000085
is a known initial value of the total active power of the distributed power supply, gammakWeighting the participation coefficient, k, for each generatorgIs a scalar quantity, η, to be calculated1,kActive power efficiency of distributed power supply k to account for inverter losses, ngIs the number of distributed power supplies, one bus includes one, two or three phase nodes.
8. The method for calculating the linear power flow of the three-phase polar coordinate system applied to the active power distribution network according to claim 1, wherein: the step S3 specifically includes:
step S31: the linear power flow is calculated by a linear equation set, wherein the linear equation set is as follows:
AX＝b (24)
in the formula (25), X is a variable to be solved and comprises a node voltage amplitude and a phase angle, A is a coefficient matrix, and b is a right term;
considering the PQ node, the ZIP load and the linear power flow equation of the Yg-Yg type transformer as follows:
Figure FDA0003151905610000091
wherein,
Figure FDA0003151905610000092
[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]；
Figure FDA0003151905610000093
Figure FDA0003151905610000101
step S32: the variables to be solved in the linear power flow are the voltage amplitude and the phase angle of each node, wherein for a distribution line, the contribution of the variables to the coefficient matrix of the linear power flow comprises right expressions of formulas (5) and (6), the contribution to the right term of the linear power flow for Y-type and delta-type ZIP loads comprises right expressions of formulas (7), (8) and (14), and the contribution to the linear power flow comprises expressions of formulas (16) to (19) for a distribution transformer;
step S33: finally forming a coefficient matrix A and a right term b of a linear equation set according to a linear power flow model of each element forming the active power distribution network, and then solving the numerical value of a variable X to be solved based on an LU decomposition technology of the matrix to obtain the voltage amplitude and the phase angle of each node of the active power distribution network.
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