CN107732918A - A kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix - Google Patents
A kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian 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
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- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The present invention relates to a kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix, belong to power distribution network optimisation technique field in power system, in the present invention, it is unknown variable by increasing branch current, establish the secondary model of the equipment such as three-phase transformer, the distributed power source with coupling characteristic, split-phase pressure regulator, to ensure Hessian matrix as constant, so as to reduce the calculating time of optimal load flow, finally Optimized model is solved using Predictor Corrector prim al- dual interior point m ethod.A kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix proposed by the invention, improve existing electricity distribution network model and Load Flow Solution method, the faster power distribution network Three Phase Power Flow of solving speed is proposed, particularly suitable for the analysis of three-phase distribution net and decision-making.
Description
Technical field
It is more particularly to a kind of to be based on permanent Hai Sen the present invention relates to distribution Analysis of Isolated Net Running and control field in power system
The power distribution network three-phase optimal load flow computational methods of matrix.
Background technology
Distributed power source (Distributed Generation, DG) and the access of new adjustment equipment are transported to conventional electrical distribution net
Row control proposes new challenge, for the active distribution network containing distributed power source at high proportion and plurality of discrete adjustable device,
Optimal power flow problems need to consider the influence that DG is distributed to distribution power flow at high proportion, by optimizing adjustable device in power network
Operation reserve realizes that operating cost is minimum or loss minimization, is that a discrete variable and continuous variable coexist on the question essence
Non-convex, Nonlinear Mixed Integer Programming Problem, according to such issues that published method solves at present, solving speed is slower,
Convergence is also poor.The discrete adjustable device contained in actual power distribution network includes compensation capacitor, ULTC etc., its
Played an important role in Optimal Power Flow Problems, improvement system node voltage, reduction via net loss etc..It is existing based on improving
Some electricity distribution network model and Load Flow Solution methods, propose the faster power distribution network three-phase optimal load flow computational methods pair of solving speed
It is significant in optimization dispatching of power netwoks.
The content of the invention
It is an object of the invention to provide a kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix,
To overcome defect present in prior art.
To achieve the above object, the technical scheme is that：A kind of power distribution network three-phase based on permanent Hessian matrix is most
Excellent tidal current computing method, comprises the following steps：
Step S1：Three-phase distribution mesh element model is established, including：Three-phase transformer, three phase mains and three-phase regulator；
Step S2：Establish permanent Hessian matrix optimal load flow model；
Step S3：The optimal load flow model is solved using estimating-correcting dual interior point.
In an embodiment of the present invention, in the step S1, for the secondary mould of the three-phase transformer using Y- △ types
Type, among branch road ij add dummy node m, by transformer branch be converted to including：No-load voltage ratio is k ideal transformer branch road im
And the transformer impedance branch road mj that impedance is R+jX；Using three-phase voltage corresponding to i, m, j node and three-phase branch current as shape
State variable, no-load voltage ratio k are control variable, KCL the and KVL equations of each branch road three-phase are constraints, establish three not higher than second order
Phase transformer secondary model, and its second dervative is constant.
According to ideal transformer branch road im voltage change ratio relation, can obtain：
It can be obtained according to ideal transformer power conservation：
Then：
Handled transformer impedance branch road mj as a general impedance branch road, then：
Wherein,Represent node voltage,Branch current is represented, subscript i, j, m represent the head of three-phase transformer branch road respectively
Endpoint node and dummy node, a, b, c represent the A phases, B phases and C phases of power distribution network respectively.
In an embodiment of the present invention, in the step S1, the three phase mains uses distributed power source, and to described
Distributed power source uses order components circuit modeling,；The order components model of the distributed power source is connected to three-phase circuit, passes through
Phase sequence changes into each phase component, establishes phase-sequence coupling model.
In an embodiment of the present invention, in the step S1, by the total Injection Current of the distributed power source and port
The phase component of voltage makees unknown quantity, according to phase sequence conversion method, obtains the node voltage and branch current of each sequence of distributed power source, i.e.,
Ip,re-jIp,im、In,re+jIn,im、I0,re+jI0,im、Up,re+jUp,im、Un,re+jUn,im、U0,re+jU0,im；
Following constraint between the order components of distributed power source be present：
In formula, P, Q are respectively the active power and reactive power of distributed power source injection power distribution network, and subscript sp is represented
The control targe that each variable is specified, subscript p, n, 0 represent positive sequence, negative phase-sequence and zero sequence respectively, and subscript re and im represent real part respectively
And imaginary part；
In an embodiment of the present invention, in the step S1, the three-phase regulator uses three-phase star pressure regulator, bag
Three single-phase voltage regulators using star connection are included, three pressure regulators each change tap joint position；The three phase voltage regulating established
Device model meets below equation restriction relation：
ka=1 ± 0.00625 × Tapa
kb=1 ± 0.00625 × Tapb
kc=1 ± 0.00625 × Tapc
Wherein, k is pressure regulator no-load voltage ratio, and A, B, C and a, b, c refer to the three-phase of pressure regulator respectively；Negative sign is used to be depressured, and positive sign is used
In boosting；Tap is the position of pressure regulator tap, is controlled by voltage of the line drop compensator according to load center；Institute
It is N that line drop compensator, which is stated, by no-load voltage ratioPT:1 voltage transformer and no-load voltage ratio is 1:NCTCurrent transformer be connected to distribution wire
Lu Shang, the preset value of the line drop compensator impedance represent the equiva lent impedance from pressure regulator to load center：
One phase voltage of load center is：
In formula, subscript P represents the phase in power distribution network A, B, C three-phase.
In an embodiment of the present invention, in the step S2, using the three-phase voltage of each node and branch road three-phase current as
State variable, establishes the optimal load flow model of three-phase distribution net, and its simplified model is as follows：
obj.min.f(x)
S.t.h (x)=0
F (x) is object function in formula, and h (x) is equality constraint, and g (x) is inequality constraints.
Wherein, object function is that network total losses are minimum, as follows：
Wherein, bn is circuitry number in distribution network, and subscript br is branch number, and subscript P represents one in A, B, C three-phase
Phase, Ubr,PAnd Ibr,PThe P phase voltages and electric current of the br articles branch road are represented respectively, and branch voltage is the node voltage at the branch road both ends
Difference.
In an embodiment of the present invention, equality constraint includes in the simplified model：Transformer branch constraint, distribution
KVL the and KCL equations of the constraint of formula power branch, pressure regulator branch constraint and each impedance branch three-phase.
In an embodiment of the present invention, the transformer branch is constrained to：
And
The distributed power source branch constraint is：
The pressure regulator branch constraint is：
And
KVL the and KCL equations of each impedance branch three-phase：
Wherein, subscript n d is node serial number, and subscript br is branch number, and A is node branch road incidence matrix, ATTo associate square
The transposition of battle array, subscript P represent one in distribution system three-phase；
In an embodiment of the present invention, inequality constraints condition includes state variable constraint and controlled in the simplified model
Variable bound；
The state variable constraint includes：Each generated power and idle units limits, node voltage amplitude constraint, it is as follows
It is shown；
The control variables constraint includes：Load tap changer gear KT, pressure regulator tap gear KV, reactive-load compensation electricity
Container switching capacity QC, it is as follows：
Compared to prior art, the invention has the advantages that：One kind proposed by the invention is based on permanent Hai Sen
The power distribution network three-phase optimal load flow computational methods of matrix, improve existing electricity distribution network model and Load Flow Solution method, propose to ask
The faster power distribution network Three Phase Power Flow of speed is solved, particularly suitable for the analysis of three-phase distribution net and decision-making.
Brief description of the drawings
Fig. 1 is a kind of flow of the power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix in the present invention
Figure.
Fig. 2 is three-phase transformer equivalent model schematic diagram in one embodiment of the invention.
Fig. 3 is three-phase star pressure regulator wiring diagram in one embodiment of the invention.
Fig. 4 is three-phase regulator schematic diagram in one embodiment of the invention.
Fig. 5 is IEEE13 node regulations system wiring figure in one embodiment of the invention.
Embodiment
Below in conjunction with the accompanying drawings, technical scheme is specifically described.
The present invention proposes a kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix, and it implements structure
As shown in figure 1, comprise the following steps：
Step S1：Three-phase distribution mesh element model is established, mainly includes three-phase transformer, three phase mains and three-phase here and adjusts
Depressor；
Further, in the present embodiment, in addition to：Step S101：The secondary model of three-phase transformer is established, passes through increasing
Branch current is added Hessian matrix in optimal load flow calculating process is become constant as unknown variable.
As shown in Fig. 2 be Y- △ type transformer branch ij, dummy node m is added in centre, make transformer branch become by
No-load voltage ratio is k ideal transformer branch road imWith the combination that impedance is this two branch roads of R+jX transformer impedance branch road mj.
According to ideal transformer branch road im voltage change ratio relation, can obtain：
It can be obtained according to ideal transformer power conservation：
Then：
Transformer impedance branch road mj can be handled as a general impedance branch road, there is the establishment of (4) formula：
Wherein,Represent node voltage,Branch current is represented, subscript i, j, m represent the head of three-phase transformer branch road respectively
Endpoint node and dummy node, a, b, c represent the A phases, B phases and C phases of power distribution network respectively.
In the present embodiment, in the transformer model, for the node i in Fig. 2, m, j three-phase voltage and three-phase branch
Road electric current is state variable, and corresponding traditional model, it is state variable to add three-phase branch current, and transformer voltage ratio k is
Variable is controlled, constraints is KCL the and KVL equations of each branch road three-phase, thus form the three-phase transformer not higher than second order
Secondary model, its second dervative are constant, so as to constitute a part for the permanent Hessian matrix of optimal load flow model.
Further, in addition to：Step S102：Establish distributed power source (DG) triphase flow.
In the present embodiment, the DG of three-phase typically sets up order components circuit modeling.DG order components model is connected to three
Circuitry phase, each phase component is changed into by phase sequence, establish phase-sequence coupling model.
In the present embodiment, to obtain DG secondary model, the phase component of the total Injection Currents of DG and port voltage is chosen
For unknown quantity, according to phase sequence conversion formula, the node voltage and branch current of each sequences of DG, i.e. I can be obtainedp,re-jIp,im、In,re
+jIn,im、I0,re+jI0,im、Up,re+jUp,im、Un,re+jUn,im、U0,re+jU0,im。
DG order components constraint is as follows：
In formula, P, Q are respectively the active power and reactive power of distributed power source injection power distribution network, and subscript sp is represented
The control targe that each variable is specified, subscript p, n, 0 represent positive sequence, negative phase-sequence and zero sequence respectively, and subscript re and im represent real part respectively
And imaginary part；
DG equality constraints equation (5) (6) (7) considers the characteristics of three phase power coupling, non-coupled different from traditional DG three-phases
Model.The DG equations are linear quadratic equations, therefore can ensure the Hai Sen in the optimal load flow calculating process containing DG
Matrix is constant.
Further, in addition to：Step S103：Establish three-phase regulator model.
In the present embodiment, three-phase star pressure regulator is made up of three single-phase voltage regulator star connections, and three pressure regulators are each
From tap joint position is changed, as shown in figure 3, the model meets below equation restriction relation：
In formula, k is pressure regulator no-load voltage ratio, and A, B, C and a, b, c refer to the three-phase of pressure regulator respectively；Negative sign is used to be depressured, and positive sign is used
In boosting；Tap is the position of pressure regulator tap, is to be controlled by line drop compensator according to the voltage of load center,
Generally there are 32 grades of regulations, adjustable range is ± 10%；Compensator is N by no-load voltage ratioPT:1 voltage transformer and no-load voltage ratio is 1:NCT
Current transformer be connected on distribution line, the setting value of compensator impedance represents the equivalent resistance from pressure regulator to load center
Anti-, formula is as follows：
The voltage of load center is：
Wherein, subscript P represents the phase in power distribution network A, B, C three-phase.
If the voltage level of load center is 120V, with a width of 2V, then pressure regulator tap gear often changes one grade, electricity
Pressure will change 0.75V, and the number that boosting, decompression time-division contact change is approximately (by taking A phases as an example)：
Or
Further, step S2：Establish permanent Hessian matrix optimal load flow model.
Using the three-phase voltage of each node and branch road three-phase current as state variable, the optimal load flow mould of three-phase distribution net is established
Type.Its simplified model is as follows：
Wherein, object function is that network total losses are minimum, as shown in formula (15).
In formula, bn is circuitry number in distribution network, and subscript br is branch number, and subscript P represents A, B, one in C three-phases
Phase, Ubr,xAnd Ibr,xThe P phase voltages and electric current of the br articles branch road are represented respectively.Branch voltage is the node voltage at the branch road both ends
Difference.
Further, following items are included for formula (14), equality constraint：
(1) transformer branch constrains, as shown in formula (1), (3), (4)；
(2) DG branch constraints, as shown in formula (5), (6), (7)；
(3) pressure regulator branch constraint, as shown in formula (8), (9)；
(4) KVL the and KCL equations of each impedance branch three-phase, as shown in formula (16).
Wherein, nd is node serial number, and br is branch number, and A is node branch road incidence matrix, ATFor turning for incidence matrix
Put, subscript P represents one in distribution system three-phase.
Further, for formula (14), inequality constraints condition includes state variable constraint and control variables constraint, respectively
For：
1) state variable constrains, containing each generated power and idle units limits, node voltage amplitude constraint, such as formula (17)
It is shown；
2) control variables constraint, including load tap changer gear KT, pressure regulator tap gear KV, reactive compensation capacitor
Device switching capacity QC, as shown in formula (18).
As can be seen here, the top step number of each formula is no more than second order in the model.
Step S3：The model is solved using estimating-correcting prim al- dual interior point m ethod, because each formula is most in model
High exponent number is no more than second order.Therefore, by using when estimating-correct prim al- dual interior point m ethod the model being solved, its Hai Sen
Matrix is constant matrix.The present embodiment use have the advantages that fast convergence rate, stability it is good estimate-correct point in former antithesis
Method solves to Optimized model.
In order to allow those skilled in the art to further appreciate that technical scheme proposed by the invention, with reference to specific implementation
Example illustrates.
By taking the amendment power distribution network IEEE13 bus test systems shown in Fig. 5 as an example, illustrate the related improved model of the present invention, calculation
The validity of method.The line parameter circuit value marked in Fig. 5 eliminates mutual impedance and admittance parameter, and the variable that controls in example is generator
It is idle contribute, DG contributes, the adjustment of transformer voltage ratio and reactive-load compensation capacitor (phase-splitting capacitor of node 8 and node 12)
Switching, wherein transformer voltage ratio and capacitor are discrete control variables.If transformer voltage ratio scope is 0.90~1.10, it is divided into
8 grades, classification step-length is 0.025.Maximum idle contribute of capacitor is 0.02pu, and classification step-length is 0.01pu.All nodes
Voltage range is 0.9~1.1pu.Pressure regulator tap has 32 grades of regulations, and adjustable range is ± 10%, the voltage water of load center
Put down as 120V, with a width of 2V.
(1) three phase-change pressures for being proposed in the conventional three-phase transformer non-quadratic function model and the present embodiment of three-phase distribution net
Device secondary model, optimal load flow calculating is carried out using the prim al- dual interior point m ethod of estimating-correct based on quadratic penalty function, as a result such as table
Shown in 1.
The different transformer model optimum results of table 1
As shown in Table 1, the via net loss using two kinds of models is identical, but it is secondary that three-phase transformer is carried in the present embodiment
Model substantially increases calculating speed compared with non-quadratic function model.
(2) in order to compare the convergence property of quadratic penalty function and Gauss penalty function and calculating time shadow to optimized algorithm
Ring, devise embedded quadratic penalty function estimate-correct prim al- dual interior point m ethod (method A) and be embedded in the estimating of Gauss penalty function-
The optimal load flow contrast test of prim al- dual interior point m ethod (method B) is corrected, as a result such as table 2.
The optimum results of table 2 contrast
Above is presently preferred embodiments of the present invention, all changes made according to technical solution of the present invention, caused function are made
During with scope without departing from technical solution of the present invention, protection scope of the present invention is belonged to.
Claims (5)
1. a kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix, it is characterised in that including following step
Suddenly：
Step S1：Three-phase distribution mesh element model is established, including：Three-phase transformer, three phase mains and three-phase regulator；
Step S2：Establish permanent Hessian matrix optimal load flow model；
Step S3：The optimal load flow model is solved using estimating-correcting dual interior point.
2. a kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix according to claim 1, its
It is characterised by, in the step S1, for the secondary model of the three-phase transformer using Y- △ types, is added among branch road ij
Dummy node m, by transformer branch be converted to including：No-load voltage ratio is k ideal transformer branch road imWith the transformation that impedance is R+jX
Device impedance branch mj；Using three-phase voltage corresponding to i, m, j node and three-phase branch current as state variable, no-load voltage ratio k becomes for control
Amount, KCL the and KVL equations of each branch road three-phase are constraints, establish the three-phase transformer secondary model not higher than second order, and its
Second dervative is constant；
In the step S1, for the secondary model of the three-phase transformer using Y- △ types, according to ideal transformer branch road im electricity
Buckling obtains than relation：
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<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>i</mi>
<mi>b</mi>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msubsup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>m</mi>
<mrow>
<mi>b</mi>
<mi>c</mi>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>k</mi>
<msubsup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>i</mi>
<mi>c</mi>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msubsup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>m</mi>
<mrow>
<mi>c</mi>
<mi>a</mi>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Handled transformer impedance branch road mj as a general impedance branch road, then：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>m</mi>
<mi>a</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>j</mi>
<mi>a</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>j</mi>
</mrow>
<mi>a</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>R</mi>
<mi>a</mi>
</msub>
<mo>+</mo>
<msub>
<mi>jX</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>m</mi>
<mi>b</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>j</mi>
<mi>b</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>j</mi>
</mrow>
<mi>b</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>R</mi>
<mi>b</mi>
</msub>
<mo>+</mo>
<msub>
<mi>jX</mi>
<mi>b</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>m</mi>
<mi>c</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>j</mi>
<mi>c</mi>
</msubsup>
<mo>=</mo>
<msubsup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>m</mi>
<mi>j</mi>
</mrow>
<mi>c</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>R</mi>
<mi>c</mi>
</msub>
<mo>+</mo>
<msub>
<mi>jX</mi>
<mi>c</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein,Represent node voltage,Branch current is represented, subscript i, j, m represent the first and last end of three-phase transformer branch road respectively
Node and dummy node, a, b, c represent the A phases, B phases and C phases of power distribution network respectively.
3. a kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix according to claim 1, its
It is characterised by, in the step S1, the three phase mains uses distributed power source, and to the distributed power source using sequence point
Measure circuit modeling；The order components model of the distributed power source is connected to three-phase circuit, and each phase component is changed into by phase sequence,
Establish phase-sequence coupling model；
In the step S1, the phase component of the total Injection Current of the distributed power source and port voltage is made into unknown quantity, root
According to phase sequence conversion method, the node voltage and branch current of each sequence of distributed power source, i.e. I are obtainedp,re-jIp,im、In,re+jIn,im、
I0,re+jI0,im、Up,re+jUp,im、Un,re+jUn,im、U0,re+jU0,im；
Following constraint between the order components of distributed power source be present：
<mrow>
<msubsup>
<mi>P</mi>
<mi>p</mi>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jQ</mi>
<mi>p</mi>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>jU</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>jI</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>I</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jI</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>U</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>jU</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>R</mi>
<mi>n</mi>
</msub>
<mo>+</mo>
<msub>
<mi>jX</mi>
<mi>n</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>jI</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
</msub>
</mrow>
<mrow>
<msubsup>
<mi>I</mi>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jI</mi>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>U</mi>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>jU</mi>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>R</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<msub>
<mi>jX</mi>
<mn>0</mn>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<msub>
<mi>I</mi>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>jI</mi>
<mrow>
<mn>0</mn>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
</msub>
</mrow>
In formula, P, Q are the active power and reactive power that distributed power source injects power distribution network, and subscript sp represents each variable and referred to
Fixed control targe, subscript p, n, 0 represent positive sequence, negative phase-sequence and zero sequence respectively, and subscript re and im represent real and imaginary parts respectively.
4. a kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix according to claim 1, its
It is characterised by, in the step S1, the three-phase regulator uses three-phase star pressure regulator, including three using star connection
Individual single-phase voltage regulator, three pressure regulators each change tap joint position；The three-phase regulator model established meets below equation
Restriction relation：
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>A</mi>
</msup>
<mo>=</mo>
<msub>
<mi>k</mi>
<mi>a</mi>
</msub>
<msup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>a</mi>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>B</mi>
</msup>
<mo>=</mo>
<msub>
<mi>k</mi>
<mi>b</mi>
</msub>
<msup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>b</mi>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>C</mi>
</msup>
<mo>=</mo>
<msub>
<mi>k</mi>
<mi>c</mi>
</msub>
<msup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>c</mi>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mi>a</mi>
</msub>
<msup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>A</mi>
</msup>
<mo>=</mo>
<msup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>a</mi>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mi>b</mi>
</msub>
<msup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>B</mi>
</msup>
<mo>=</mo>
<msup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>b</mi>
</msup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mi>c</mi>
</msub>
<msup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>C</mi>
</msup>
<mo>=</mo>
<msup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>c</mi>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mi>a</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>&PlusMinus;</mo>
<mn>0.00625</mn>
<mo>&times;</mo>
<msub>
<mi>Tap</mi>
<mi>a</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mi>b</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>&PlusMinus;</mo>
<mn>0.00625</mn>
<mo>&times;</mo>
<msub>
<mi>Tap</mi>
<mi>b</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>k</mi>
<mi>c</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>&PlusMinus;</mo>
<mn>0.00625</mn>
<mo>&times;</mo>
<msub>
<mi>Tap</mi>
<mi>c</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, k is pressure regulator no-load voltage ratio, and A, B, C and a, b, c refer to the three-phase of pressure regulator respectively；Negative sign is used to be depressured, and positive sign is used to rise
Pressure；Tap is the position of pressure regulator tap, is controlled by voltage of the line drop compensator according to load center；The line
No-load voltage ratio is N by road voltage drop compensatorPT:1 voltage transformer and no-load voltage ratio is 1:NCTCurrent transformer be connected to distribution line
On, the preset value of the line drop compensator impedance represents the equiva lent impedance from pressure regulator to load center：
<mrow>
<msup>
<mi>R</mi>
<mo>&prime;</mo>
</msup>
<mo>+</mo>
<msup>
<mi>jX</mi>
<mo>&prime;</mo>
</msup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mi>R</mi>
<mo>+</mo>
<mi>j</mi>
<mi>X</mi>
<mo>)</mo>
</mrow>
<mfrac>
<msub>
<mi>N</mi>
<mrow>
<mi>C</mi>
<mi>T</mi>
</mrow>
</msub>
<msub>
<mi>N</mi>
<mrow>
<mi>P</mi>
<mi>T</mi>
</mrow>
</msub>
</mfrac>
</mrow>
One phase voltage of load center is：
<mrow>
<msubsup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>l</mi>
<mi>o</mi>
<mi>a</mi>
<mi>d</mi>
</mrow>
<mi>P</mi>
</msubsup>
<mo>=</mo>
<mfrac>
<msup>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>P</mi>
</msup>
<msub>
<mi>N</mi>
<mrow>
<mi>P</mi>
<mi>T</mi>
</mrow>
</msub>
</mfrac>
<mo>-</mo>
<mrow>
<mo>(</mo>
<msup>
<mi>R</mi>
<mo>&prime;</mo>
</msup>
<mo>+</mo>
<msup>
<mi>jX</mi>
<mo>&prime;</mo>
</msup>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<mfrac>
<msup>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mi>P</mi>
</msup>
<msub>
<mi>N</mi>
<mrow>
<mi>C</mi>
<mi>T</mi>
</mrow>
</msub>
</mfrac>
</mrow>
Wherein, subscript P represents the phase in power distribution network A, B, C three-phase.
5. a kind of power distribution network three-phase optimal load flow computational methods based on permanent Hessian matrix according to claim 1, its
It is characterised by, in the step S2, using the three-phase voltage of each node and branch road three-phase current as state variable, establishes three matchings
The optimal load flow model of power network, its simplified model are as follows：
obj.min.f(x)
S.t.h (x)=0
<mrow>
<munder>
<mi>g</mi>
<mo>&OverBar;</mo>
</munder>
<mo>&le;</mo>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>&le;</mo>
<mover>
<mi>g</mi>
<mo>&OverBar;</mo>
</mover>
</mrow>
F (x) is object function in formula, and h (x) is equality constraint, and g (x) is inequality constraints；
Wherein, object function is that network total losses are minimum, as follows：
<mrow>
<mi>min</mi>
<mi> </mi>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>l</mi>
<mi>o</mi>
<mi>s</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>b</mi>
<mi>r</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>b</mi>
<mi>n</mi>
</mrow>
</munderover>
<munder>
<mo>&Sigma;</mo>
<mrow>
<mi>P</mi>
<mo>=</mo>
<mo>{</mo>
<mi>A</mi>
<mo>,</mo>
<mi>B</mi>
<mo>,</mo>
<mi>C</mi>
<mo>}</mo>
</mrow>
</munder>
<msub>
<mover>
<mi>U</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>r</mi>
<mo>,</mo>
<mi>P</mi>
</mrow>
</msub>
<msup>
<msub>
<mover>
<mi>I</mi>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<mi>b</mi>
<mi>r</mi>
<mo>,</mo>
<mi>P</mi>
</mrow>
</msub>
<mo>*</mo>
</msup>
</mrow>
Wherein, bn is circuitry number in distribution network, and subscript br is branch number, and subscript P represents A, B, the phase in C three-phases, Ubr,x
And Ibr,xThe P phase voltages and electric current of the br articles branch road are represented respectively, and branch voltage is the difference of the node voltage at the branch road both ends；
Equality constraint includes in the simplified model：Transformer branch constraint, distributed power source branch constraint, pressure regulator branch
Road constrains and KVL the and KCL equations of each impedance branch three-phase；
The transformer branch is constrained to：
And
The distributed power source branch constraint is：
<mrow>
<msubsup>
<mi>P</mi>
<mi>p</mi>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jQ</mi>
<mi>p</mi>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>=</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>U</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>jU</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>I</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>jI</mi>
<mrow>
<mi>p</mi>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>I</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>jI</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>i</mi>
<mi>m</mi>
</mrow>
<mrow>
<mi>s</mi>
<mi>p</mi>
</mrow>
</msubsup>
<mo>-</mo>
<mfrac>
<mrow>
<msub>
<mi>U</mi>
<mrow>
<mi>n</mi>
<mo>,</mo>
<mi>r</mi>
<mi>e</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>jU</mi>
<mrow>
<mi>n</mi>
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The pressure regulator branch constraint is：
And
KVL the and KCL equations of each impedance branch three-phase：
Ubr,P,re=AUnd,P,re
Ubr,P,im=AUnd,P,im
0=ATIbr,P,re
0=ATIbr,P,im
Wherein, nd is node serial number, and br is branch number, and A is node branch road incidence matrix, ATFor the transposition of incidence matrix, subscript
P represents one in distribution system three-phase；
Inequality constraints condition includes state variable constraint and control variables constraint in the simplified model；
The state variable constraint includes：Each generated power PGi,P, idle output QGi,PAnd node voltage amplitude Ui,P, following institute
Show：
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The control variables constraint includes：Load tap changer gear KT, pressure regulator tap gear KV, reactive-load compensation capacitor
Switching capacity QC, it is as follows：
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