CN107451685A - A kind of distribution network planning LCC models based on power distribution automation - Google Patents

A kind of distribution network planning LCC models based on power distribution automation Download PDF

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CN107451685A
CN107451685A CN201710587258.XA CN201710587258A CN107451685A CN 107451685 A CN107451685 A CN 107451685A CN 201710587258 A CN201710587258 A CN 201710587258A CN 107451685 A CN107451685 A CN 107451685A
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汪新武
郭创新
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Guangdong Shuang Xin Electric Technology Co Ltd
Huanan Industrial Technology Research Institute of Zhejiang University
Industrial Technology Research Institute of ZJU
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Huanan Industrial Technology Research Institute of Zhejiang University
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    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
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Abstract

The invention discloses a kind of distribution network planning LCC models based on power distribution automation.The problem to be solved in the present invention is, in face of the grid-connected quantity of the distributed power source increased year by year, the target that totle drilling cost is minimum in the cycle of operation to be reached in the environment of power distribution automation.The present invention sets logical variable first in targeting scheme design, then the construction plan of cycle of operation internal segment point load, distributed energy access prediction and transformer station is obtained, the condition of information above is finally added in LCC object function and constraints, the distribution network planning LCC models based on power distribution automation can be obtained.The present invention establishes life cycle cost LCC functions, add discount factor, it is contemplated that the time cost of fund, longer-term are comprehensively calculated various costs in life cycle, the object function of profit maximization is added simultaneously, and the economical of distribution planning is considered from different aspect；The present invention is a kind of comprehensive, economic, reliable distribution network planning model.

Description

A kind of distribution network planning LCC models based on power distribution automation
Technical field
The present invention relates to the planning for determining power distribution network, belong to intelligent grid field, and in particular to one kind is automatic based on distribution The distribution network planning LCC models of change.
Technical background
Modern power distribution net utilizes a large amount of intelligent electronic devices, in the case of no human intervention, to operation of power networks state Monitor and assess in real time.Power distribution network can diagnose early warning before failure in the environment of power distribution automation to it, right after failure It positions isolation, so as to ensure power network safety operation and the reliable electricity consumption of user.
Distributed energy has the advantages that environment-friendly, peak regulation is convenient, investment construction is few, with large-scale distributed power supply It is grid-connected, the planning on power distribution network also generates certain influence.
Distribution network planning is on the basis of existing network, according to the result to planning period load prediction, is meeting to bear On the premise of lotus demand and electricity consumption reliability, an optimal construction scheme is determined, to reach the requirement of object function.Planning side Case includes：1. reasonably select circuit；2. built, removed or reinforced after determining the position of transformer station, model and capacity Work.The distribution network structure building time cycle is longer, it is necessary to which programme is divided into multiple stages implementations, and service life week Current cost LCC functions, consider time value on assets, add discount factor, synthetically calculate each stage construction, operation, dimension The cost of shield etc., so as to obtain most economical programme.
In distribution network planning model based on power distribution automation, various distributing automation apparatus are not only allowed for, herein in connection with The influence of distributed power source, based on life cycle cost, the fairly comprehensive consideration model of planning.
The content of the invention
The problem to be solved in the present invention is, in face of the grid-connected quantity of the distributed power source increased year by year, in power distribution automation Environment in reach the minimum target of totle drilling cost in the cycle of operation.The present invention is in targeting scheme design, it is proposed that one kind is based on The distribution network planning LCC models of power distribution automation.Logical variable is set first, cycle of operation internal segment point load is then obtained, divides Cloth energy access prediction and the construction plan of transformer station, finally in LCC object function and constraints more than addition The condition of information, the distribution network planning LCC models based on power distribution automation can be obtained.
To solve technical problem, solution of the invention comprises the following steps：
Step (1) sets logical variable xi,k；
Because programme is generally divided into time and two, space dimension, therefore logical variable includes default feeder line, power transformation Stand or two key elements of the numbering of distributed power source and time.Then cycle of operation internal segment point load, distributed energy access are obtained Prediction and the construction plan of transformer station.
Step (2) forms object function LCC；
Calculate initial investment cost CI, operating cost CO, maintenance cost CM, power failure cost CF, put processing cost CD aside as useless.Meter The discount factor for calculating initial investment is PVI, operation cost discount factor PVsum, put the discount factor P of processing cost aside as uselessVD.Establish The life cycle cost function LCC and object function maxProfit=Rev-LCC of profit maximization.
Step (3) forms constraints；
The conditions such as network constraint, electrical constraints, logical constraint are determined according to the characteristics of network.
Step (4) solves the model with genetic algorithm.
The step (1) is accomplished in the following manner：
1-1. setting the logical variable that can be applied to the model, the logical variable includes default feeder line, transformer station or distribution Two key elements of numbering and time of formula power supply.
If xi,kRepresent the action of the predicted elemental of kth stage i-th.
When element i is transformer station, xi,k=1 expression stage k adds a transformer in transformer station i；xi,k=0 expression rank It is unchanged in section k transformer station i.When element i is feeder line, xi,k=1 expression stage k has set up i feeder lines；xi,k=0 represents stage k Middle i feeder lines do not change；And xi,k=-1 represents that i feeder lines are removed in stage k.When element i is DG, xi,k=1 represents rank Section k is incorporated with i DG；xi,kI DG do not change in=0 expression stage k.
If Xi,kFor stage k predicted elemental i state, Xi,kI elements have been built in network during=1 expression stage k, and Xi,k=0 expression stage k when i elements do not built, or (feeder line) set up after be removed.
1-2. obtains the construction plan of cycle of operation internal segment point load, distributed energy access prediction and transformer station.
Cycle of operation interior nodes load prediction should include two key elements of node location and payload；Distributed energy accesses Prediction data should include two key elements of node location and mean power；Transformer substation construction planning should include node location and transformer station Two key elements of capacity.
The step (2) is accomplished in the following manner：
2-1. calculate initial investment cost CI, for concentrate pay in a short time purchase, mounting cost, its computational methods is such as Under：
Wherein：Ns is transformer station's quantity；Nl is number of, lines；Nb is load bus quantity；α is discount rate；CIsubTo become Power station initial investment expense, CIDGFor DG initial investment expenses；LiFor i section line lengths；CIlFor every km circuit cost, unit For member/km；CIbrk、CIrcl、CIfuse、CIcpt、CIswt、CIFPIRespectively breaker, reclosing, fuse, capacitor, isolation Switch, the initial investment expense of failure traffic indicator；Xbrki、Xrcli、Xfusei、Xcpti、Xswti、XFPIiRespectively the i-th circuit/ Breaker, reclosing, fuse, capacitor, disconnecting switch, the existence of failure traffic indicator, X in load bus*=1 Expression is present in circuit/node, X*=0 represents to be not present in circuit/node.
2-2. calculates operating cost CO, including electric energy loss during operation of power networks and the operating cost of transformer station, and it is calculated Method is as follows：
Wherein Pli(k) it is kth stage circuit i line loss；CkWhFor electricity price, unit is member/kWh；Ssi(k) it is k stages i Number substation capacity, unit kVA；COsubFor substation operation expense, unit is member/kVA.
2-3. calculates maintenance cost CM, includes the maintenance cost of transformer station, cable and each protection device, its computational methods It is as follows：
Wherein CMsubFor transformer station's maintenance cost, unit is member/kVA, CM*Represent that related device year safeguards in the kth stage Expense, unit are member.
2-4. calculates power failure cost CF, this is defined herein as Custom interruption cost, its computational methods is as follows：
Wherein λiFor circuit i fault rate, can be reduced to fix same value in model；T is line fault recovery time, should Value is determined by each protection device performance parameter；Nbi is the load bus quantity in faulty line i；ESij(k) it is load in circuit i Node j power；ESi(k) it is the power of all loads in circuit i；PDGij(k)For the average work(of DG on load bus j in circuit i Rate；VLijFor the Custom interruption cost expense of load bus j in circuit i, unit is member/kW.
2-5. is calculated and is put processing cost CD aside as useless, and its computational methods is as follows：
Wherein CDlFor the processing cost of putting aside as useless of circuit, unit is member/km.
2-6. calculates the discount factor of initial investment：
Wherein y (k) matches somebody with somebody the year of network operation before representing k-th of stage.PVIMeaning be discount rate be α situation Under, the currency after y (k) years is discounted into the coefficient of present worth.
2-7. calculates the discount factor of kth stage operation cost：
Wherein d (k) is the time cycle in kth stage.
2-8. calculates the discount factor for putting processing cost aside as useless in the kth stage：
2-9. calculates power selling income Rev, and calculation formula is
W in formulaD(t) the average electricity consumption aggregate demand for being t in network, WDG(t) the average DG hairs for being t in network Electricity, unit kW.
2-10. obtains life cycle cost function and profit maximum target function, wherein life cycle cost function： LCC=PVICI+PVsum(CO+CM+CF)+PVDCD；Profit maximum target function：MaxProfit=Rev-LCC.
The step (3), which is accomplished in the following manner, sets constraints：
It is 3-1. connective
Each load point must be connected by feeder line and networked in network, and without acnode, that is, network is connection.
It is 3-2. radial
To ensure distribution network safe and reliable operation, it is necessary to make the radial open loop operation of network.Necessary and sufficient condition is
Nl=nb-1
I.e. circuit number is that load points subtract 1.
3-3. trend constraint
PiRepresent the active injection power of node i；QiRepresent the idle injecting power of node i；ViRepresent the voltage of node i； VjRepresent node j voltage；θijRepresent the phase difference of voltage between node i and j；GijRepresent the conductance on circuit ij；BijRepresent Susceptance on circuit ij.
3-4. node voltage scopes
Vmin≤Vi≤Vmax
VminAnd VmaxThe minimum value and maximum of node voltage are referred to respectively；
3-5. capacity limit
For transformer station, DG and feeder line, have
PiRepresent the active power of each node；QiRepresent the reactive power of each node；SimaxRepresent regarding for each node In power maximum.
3-6 logical variables constrain
To meet the feasibility of scheme implementation, there is following limitation to logical variable：
NsmaxRepresent that i transformer stations maximum can load the quantity of transformer, first formula is limited in a transformer station The quantity of transformer.Lf represents the set of default circuit in network, and le represents to have set up the set of circuit.Second and third public affairs Formula limits the feeder line at most installation one of same position.
The present invention has the beneficial effect that：
The present invention establishes life cycle cost LCC functions, adds discount factor, it is contemplated that the time cost of fund, Longer-term is more fully calculated various costs in life cycle, while adds the object function of profit maximization, can To consider the economical of distribution planning from different aspect；Add breaker, reclosing, fuse, capacitor, disconnecting switch, The distributing automation apparatus such as failure traffic indicator, improve system reliability, greatly reduce user caused by grid cut-off Power failure cost；Effect of the distributed power source in power distribution network is considered simultaneously, being generated electricity in power network normal operation for user produces Income, the timely power transmission in grid collapses, reduce user's power failure cost.To sum up, this model be it is a kind of comprehensively, it is economical, can The distribution network planning model leaned on.
Embodiment
With reference to embodiment, the invention will be further described.In face of the distributed power source and netting index increased year by year Amount, the target that totle drilling cost is minimum in the cycle of operation is reached in the environment of power distribution automation.The present invention targeting scheme design in, Logical variable is set first, then obtains building for cycle of operation internal segment point load, distributed energy access prediction and transformer station If planning, the condition of information above is finally added in LCC object function and constraints, can obtain being based on power distribution automation Distribution network planning LCC models.
A kind of distribution network planning LCC models based on power distribution automation, comprise the following steps：
Step (1) sets logical variable xi,k；
Because programme is generally divided into time and two, space dimension, therefore logical variable includes default feeder line, power transformation Stand or two key elements of the numbering of distributed power source and time.Then cycle of operation internal segment point load, distributed energy access are obtained Prediction and the construction plan of transformer station.
Step (2) forms object function LCC；
Calculate initial investment cost CI, operating cost CO, maintenance cost CM, power failure cost CF, put processing cost CD aside as useless.Meter The discount factor for calculating initial investment is PVI, operation cost discount factor PVsum, put the discount factor P of processing cost aside as uselessVD.Establish The life cycle cost function LCC and object function maxProfit=Rev-LCC of profit maximization.
Step (3) forms constraints；
The conditions such as network constraint, electrical constraints, logical constraint are determined according to the characteristics of network.
Step (4) solves the model with genetic algorithm.
The step (1) is accomplished in the following manner：
1-1. sets the logical variable that can be applied to the model, and the logical variable includes default feeder line, transformer station or distribution Two key elements of numbering and time of formula power supply.
If xi,kRepresent the action of the predicted elemental of kth stage i-th.
When element i is transformer station, xi,k=1 expression stage k adds a transformer in transformer station i；xi,k=0 expression rank It is unchanged in section k transformer station i.When element i is feeder line, xi,k=1 expression stage k has set up i feeder lines；xi,k=0 represents stage k Middle i feeder lines do not change；And xi,k=-1 represents that i feeder lines are removed in stage k.When element i is DG, xi,k=1 represents rank Section k is incorporated with i DG；xi,kI DG do not change in=0 expression stage k.
If Xi,kFor stage k predicted elemental i state, Xi,kI elements have been built in network during=1 expression stage k, and Xi,k=0 expression stage k when i elements do not built, or (feeder line) set up after be removed.
1-2. obtains the construction plan of cycle of operation internal segment point load, distributed energy access prediction and transformer station.
Cycle of operation interior nodes load prediction should include two key elements of node location and payload；Distributed energy accesses Prediction data should include two key elements of node location and mean power；Transformer substation construction planning should include node location and transformer station Two key elements of capacity.
The step (2) is accomplished in the following manner：
2-1. calculate initial investment cost CI, for concentrate pay in a short time purchase, mounting cost, its computational methods is such as Under：
Wherein：Ns is transformer station's quantity；Nl is number of, lines；Nb is load bus quantity；α is discount rate；CIsubTo become Power station initial investment expense, CIDGFor DG initial investment expenses；LiFor i section line lengths；CIlFor every km circuit cost, unit For member/km；CIbrk、CIrcl、CIfuse、CIcpt、CIswt、CIFPIRespectively breaker, reclosing, fuse, capacitor, isolation Switch, the initial investment expense of failure traffic indicator；Xbrki、Xrcli、Xfusei、Xcpti、Xswti、XFPIiRespectively the i-th circuit/ Breaker, reclosing, fuse, capacitor, disconnecting switch, the existence of failure traffic indicator, X in load bus*=1 Expression is present in circuit/node, X*=0 represents to be not present in circuit/node.
2-2. calculates operating cost CO, including electric energy loss during operation of power networks and the operating cost of transformer station, and it is calculated Method is as follows：
Wherein Pli(k) it is kth stage circuit i line loss；CkWhFor electricity price, unit is member/kWh；Ssi(k) it is k stages i Number substation capacity, unit kVA；COsubFor substation operation expense, unit is member/kVA.
2-3. calculates maintenance cost CM, includes the maintenance cost of transformer station, cable and each protection device, its computational methods It is as follows：
Wherein CMsubFor transformer station's maintenance cost, unit is member/kVA, CM*Represent that related device year safeguards in the kth stage Expense, unit are member.
2-4. calculates power failure cost CF, this is defined herein as Custom interruption cost, its computational methods is as follows：
Wherein λiFor circuit i fault rate, can be reduced to fix same value in model；T is line fault recovery time, should Value is determined by each protection device performance parameter；Nbi is the load bus quantity in faulty line i；ESij(k) it is load in circuit i Node j power；ESi(k) it is the power of all loads in circuit i；PDGij(k)For the average work(of DG on load bus j in circuit i Rate；VLijFor the Custom interruption cost expense of load bus j in circuit i, unit is member/kW.
2-5. is calculated and is put processing cost CD aside as useless, and its computational methods is as follows：
Wherein CDlFor the processing cost of putting aside as useless of circuit, unit is member/km.
2-6. calculates the discount factor of initial investment：
Wherein y (k) matches somebody with somebody the year of network operation before representing k-th of stage.PVIMeaning be discount rate be α situation Under, the currency after y (k) years is discounted into the coefficient of present worth.
2-7. calculates the discount factor of kth stage operation cost：
Wherein d (k) is the time cycle in kth stage.
2-8. calculates the discount factor for putting processing cost aside as useless in the kth stage：
2-9. calculates power selling income Rev, and calculation formula is
W in formulaD(t) the average electricity consumption aggregate demand for being t in network, WDG(t) the average DG hairs for being t in network Electricity, unit kW.
2-10. obtains life cycle cost function and profit maximum target function, wherein life cycle cost function： LCC=PVICI+PVsum(CO+CM+CF)+PVDCD；Profit maximum target function：MaxProfit=Rev-LCC.
The step (3), which is accomplished in the following manner, sets constraints：
It is 3-1. connective
Each load point must be connected by feeder line and networked in network, and without acnode, that is, network is connection.
It is 3-2. radial
To ensure distribution network safe and reliable operation, it is necessary to make the radial open loop operation of network.Necessary and sufficient condition is
Nl=nb-1
I.e. circuit number is that load points subtract 1.
3-3. trend constraint
PiRepresent the active injection power of node i；QiRepresent the idle injecting power of node i；ViRepresent the voltage of node i； VjRepresent node j voltage；θijRepresent the phase difference of voltage between node i and j；GijRepresent the conductance on circuit ij；BijRepresent Susceptance on circuit ij.
3-4. node voltage scopes
Vmin≤Vi≤Vmax
VminAnd VmaxThe minimum value and maximum of node voltage are referred to respectively；
3-5. capacity limit
For transformer station, DG and feeder line, have
PiRepresent the active power of each node；QiRepresent the reactive power of each node；SimaxRepresent regarding for each node In power maximum.
3-6 logical variables constrain
To meet the feasibility of scheme implementation, there is following limitation to logical variable：
NsmaxRepresent that i transformer stations maximum can load the quantity of transformer, first formula is limited in a transformer station The quantity of transformer.Lf represents the set of default circuit in network, and le represents to have set up the set of circuit.Second and third public affairs Formula limits the feeder line at most installation one of same position.

Claims (1)

1. a kind of distribution network planning LCC models based on power distribution automation, it is characterised in that comprise the following steps：
Step (1) sets logical variable xi,k；
Because programme is generally divided into time and two, space dimension, thus logical variable include default feeder line, transformer station or Two key elements of numbering and time of distributed power source；Then cycle of operation internal segment point load, distributed energy access prediction are obtained And the construction plan of transformer station；
Step (2) forms object function LCC；
Calculate initial investment cost CI, operating cost CO, maintenance cost CM, power failure cost CF, put processing cost CD aside as useless；Calculate just The phase discount factor of investment is PVI, operation cost discount factor PVsum, put the discount factor P of processing cost aside as uselessVD；Establish the life-span The life cycle costing function LCC and object function maxProfit=Rev-LCC of profit maximization；
Step (3) forms constraints；
The conditions such as network constraint, electrical constraints, logical constraint are determined according to the characteristics of network；
Step (4) solves the model with genetic algorithm；
The step (1) is accomplished in the following manner：
1-1. sets the logical variable that can be applied to the model, and the logical variable includes default feeder line, transformer station or distributed electrical Two key elements of numbering and time in source；
If xi,kRepresent the action of the predicted elemental of kth stage i-th；
When element i is transformer station, xi,k=1 expression stage k adds a transformer in transformer station i；xi,k=0 expression stage k It is unchanged in transformer station i；When element i is feeder line, xi,k=1 expression stage k has set up i feeder lines；xi,k=0 represents i in stage k Number feeder line does not change；And xi,k=-1 represents that i feeder lines are removed in stage k；When element i is DG, xi,k=1 represents stage k It is incorporated with i DG；xi,kI DG do not change in=0 expression stage k；
If Xi,kFor stage k predicted elemental i state, Xi,kI elements have been built in network during=1 expression stage k, and Xi,k =0 expression stage k when i elements do not built, or (feeder line) set up after be removed；
1-2. obtains the construction plan of cycle of operation internal segment point load, distributed energy access prediction and transformer station；
Cycle of operation interior nodes load prediction should include two key elements of node location and payload；Distributed energy access prediction Data should include two key elements of node location and mean power；Transformer substation construction planning should include node location and substation capacity Two key elements；
The step (2) is accomplished in the following manner：
2-1. calculates initial investment cost CI, for concentrate pay in a short time purchase, mounting cost, its computational methods is as follows：
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>C</mi> <mi>I</mi> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>s</mi> </mrow> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>&amp;alpha;</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>CI</mi> <mrow> <mi>s</mi> <mi>u</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>CI</mi> <mrow> <mi>D</mi> <mi>G</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>l</mi> </mrow> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mi>&amp;alpha;</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mo>&amp;CenterDot;</mo> <mo>(</mo> <msub> <mi>CI</mi> <mi>l</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>L</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>CI</mi> <mrow> <mi>b</mi> <mi>r</mi> <mi>k</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>b</mi> <mi>r</mi> <mi>k</mi> <mi>i</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>CI</mi> <mrow> <mi>r</mi> <mi>c</mi> <mi>l</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>r</mi> <mi>c</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>CI</mi> <mrow> <mi>f</mi> <mi>u</mi> <mi>s</mi> <mi>e</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>f</mi> <mi>u</mi> <mi>s</mi> <mi>e</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mi>CI</mi> <mrow> <mi>c</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>p</mi> <mi>t</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>CI</mi> <mrow> <mi>s</mi> <mi>w</mi> <mi>t</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>s</mi> <mi>w</mi> <mi>t</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>CI</mi> <mrow> <mi>F</mi> <mi>P</mi> <mi>I</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mi>P</mi> <mi>I</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein：Ns is transformer station's quantity；Nl is number of, lines；Nb is load bus quantity；α is discount rate；CIsubFor transformer station Initial investment expense, CIDGFor DG initial investment expenses；LiFor i section line lengths；CIlFor every km circuit cost, unit is Member/km；CIbrk、CIrcl、CIfuse、CIcpt、CIswt、CIFPIRespectively breaker, reclosing, fuse, capacitor, keep apart Close, the initial investment expense of failure traffic indicator；Xbrki、Xrcli、Xfusei、Xcpti、Xswti、XFPIiRespectively the i-th circuit/negative Lotus node interrupts road device, reclosing, fuse, capacitor, disconnecting switch, the existence of failure traffic indicator, X*=1 table Show and be present in circuit/node, X*=0 represents to be not present in circuit/node；
2-2. calculates operating cost CO, including electric energy loss during operation of power networks and the operating cost of transformer station, its computational methods It is as follows：
<mrow> <mi>C</mi> <mi>O</mi> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>l</mi> </mrow> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>0.5</mn> <mi>&amp;alpha;</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mrow> <mo>(</mo> <mrow> <msub> <mi>P</mi> <mrow> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>C</mi> <mrow> <mi>k</mi> <mi>W</mi> <mi>h</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>s</mi> </mrow> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>0.5</mn> <mi>&amp;alpha;</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>k</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>s</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>CO</mi> <mrow> <mi>s</mi> <mi>u</mi> <mi>b</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow>
Wherein Pli(k) it is kth stage circuit i line loss；CkWhFor electricity price, unit is member/kWh；Ssi(k) it is No. i change of k stages Station capacity, unit kVA；COsubFor substation operation expense, unit is member/kVA；
2-3. calculates maintenance cost CM, includes the maintenance cost of transformer station, cable and each protection device, its computational methods is such as Under：
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>C</mi> <mi>M</mi> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>s</mi> </mrow> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>0.5</mn> <mi>&amp;alpha;</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>s</mi> <mi>i</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>CM</mi> <mrow> <mi>s</mi> <mi>u</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>CM</mi> <mrow> <mi>D</mi> <mi>G</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>l</mi> </mrow> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>0.5</mn> <mi>&amp;alpha;</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mo>&amp;CenterDot;</mo> <mo>(</mo> <msub> <mi>CM</mi> <mi>l</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>L</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>CM</mi> <mrow> <mi>b</mi> <mi>r</mi> <mi>k</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>b</mi> <mi>r</mi> <mi>k</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>CM</mi> <mrow> <mi>r</mi> <mi>c</mi> <mi>l</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>r</mi> <mi>c</mi> <mi>l</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>CM</mi> <mrow> <mi>f</mi> <mi>u</mi> <mi>s</mi> <mi>e</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>f</mi> <mi>u</mi> <mi>s</mi> <mi>e</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> </mrow> </munderover> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mn>0.5</mn> <mi>&amp;alpha;</mi> </mrow> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mo>&amp;CenterDot;</mo> <mo>(</mo> <msub> <mi>CM</mi> <mrow> <mi>c</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>c</mi> <mi>p</mi> <mi>t</mi> <mi>i</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>CM</mi> <mrow> <mi>s</mi> <mi>w</mi> <mi>t</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>s</mi> <mi>w</mi> <mi>t</mi> <mi>i</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>CM</mi> <mrow> <mi>F</mi> <mi>P</mi> <mi>I</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mi>P</mi> <mi>I</mi> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein CMsubFor transformer station's maintenance cost, unit is member/kVA, CM*Related device year is represented in kth stage maintenance cost, Unit is member；
2-4. calculates power failure cost CF, this is defined herein as Custom interruption cost, its computational methods is as follows：
<mrow> <mi>C</mi> <mi>F</mi> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>l</mi> </mrow> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.5</mn> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mo>&amp;CenterDot;</mo> <msub> <mi>&amp;lambda;</mi> <mi>i</mi> </msub> <mo>&amp;CenterDot;</mo> <mi>t</mi> <mo>&amp;CenterDot;</mo> <msub> <mi>ES</mi> <mrow> <mi>i</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>&amp;CenterDot;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> <mi>i</mi> </mrow> </munderover> <msub> <mi>VL</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow>
<mrow> <msub> <mi>ES</mi> <mrow> <mi>i</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> <mi>i</mi> </mrow> </munderover> <msub> <mi>ES</mi> <mrow> <mi>i</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>-</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> <mi>i</mi> </mrow> </munderover> <msub> <mi>P</mi> <mrow> <mi>D</mi> <mi>G</mi> <mi>i</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> <mi>i</mi> </mrow> </munderover> <msub> <mi>P</mi> <mrow> <mi>D</mi> <mi>G</mi> <mi>i</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>&lt;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> <mi>i</mi> </mrow> </munderover> <msub> <mi>ES</mi> <mrow> <mi>i</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> <mi>i</mi> </mrow> </munderover> <msub> <mi>P</mi> <mrow> <mi>D</mi> <mi>G</mi> <mi>i</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>&amp;GreaterEqual;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>b</mi> <mi>i</mi> </mrow> </munderover> <msub> <mi>ES</mi> <mrow> <mi>i</mi> <mi>j</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein λiFor circuit i fault rate, can be reduced to fix same value in model；T is line fault recovery time, the value by Each protection device performance parameter determines；Nbi is the load bus quantity in faulty line i；ESij(k) it is load bus in circuit i J power；ESi(k) it is the power of all loads in circuit i；PDGij(k)For the mean power of DG on load bus j in circuit i； VLijFor the Custom interruption cost expense of load bus j in circuit i, unit is member/kW；
2-5. is calculated and is put processing cost CD aside as useless, and its computational methods is as follows：
<mrow> <mi>C</mi> <mi>D</mi> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mi>l</mi> </mrow> </munderover> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>CD</mi> <mi>l</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>L</mi> <mi>i</mi> </msub> </mrow>
Wherein CDlFor the processing cost of putting aside as useless of circuit, unit is member/km；
2-6. calculates the discount factor of initial investment：
<mrow> <msub> <mi>P</mi> <mrow> <mi>V</mi> <mi>I</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msup> </mfrac> </mrow>
Wherein y (k) matches somebody with somebody the year of network operation before representing k-th of stage；PVIMeaning be discount rate be α in the case of, y (k) currency after year discounts into the coefficient of present worth；
2-7. calculates the discount factor of kth stage operation cost：
<mrow> <msub> <mi>P</mi> <mrow> <mi>V</mi> <mi>s</mi> <mi>u</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msup> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mi>&amp;alpha;</mi> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msup> </mrow> </mfrac> </mrow> 2
Wherein d (k) is the time cycle in kth stage；
2-8. calculates the discount factor for putting processing cost aside as useless in the kth stage：
<mrow> <msub> <mi>P</mi> <mrow> <mi>V</mi> <mi>D</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mrow> <mi>d</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </msup> </mfrac> </mrow>
2-9. calculates power selling income Rev, and calculation formula is
<mrow> <mi>Re</mi> <mi>v</mi> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <mfrac> <mn>1</mn> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mn>0.5</mn> <mi>&amp;alpha;</mi> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> </mfrac> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mi>D</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>P</mi> <mrow> <mi>D</mi> <mi>G</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>C</mi> <mrow> <mi>k</mi> <mi>W</mi> <mi>h</mi> </mrow> </msub> </mrow>
W in formulaD(t) the average electricity consumption aggregate demand for being t in network, WDG(t) the average DG for being t in network generates electricity Amount, unit kW；
2-10. obtains life cycle cost function and profit maximum target function, wherein life cycle cost function：LCC= PVICI+PVsum(CO+CM+CF)+PVDCD；Profit maximum target function：MaxProfit=Rev-LCC；
The step (3), which is accomplished in the following manner, sets constraints：
It is 3-1. connective
Each load point must be connected by feeder line and networked in network, and without acnode, that is, network is connection；
It is 3-2. radial
To ensure distribution network safe and reliable operation, it is necessary to make the radial open loop operation of network；Necessary and sufficient condition is
Nl=nb-1
I.e. circuit number is that load points subtract 1；
3-3. trend constraint
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>i</mi> </msub> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mi>b</mi> </mrow> </munderover> <msub> <mi>V</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Q</mi> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>V</mi> <mi>i</mi> </msub> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mi>b</mi> </mrow> </munderover> <msub> <mi>V</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>G</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>sin&amp;theta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>B</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <msub> <mi>cos&amp;theta;</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
PiRepresent the active injection power of node i；QiRepresent the idle injecting power of node i；ViRepresent the voltage of node i；VjTable Show node j voltage；θijRepresent the phase difference of voltage between node i and j；GijRepresent the conductance on circuit ij；BijRepresent circuit Susceptance on ij；
3-4. node voltage scopes
Vmin≤Vi≤Vmax
VminAnd VmaxThe minimum value and maximum of node voltage are referred to respectively；
3-5. capacity limit
For transformer station, DG and feeder line, have
<mrow> <msubsup> <mi>P</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>Q</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>&amp;le;</mo> <msubsup> <mi>S</mi> <mrow> <mi>i</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <mn>2</mn> </msubsup> </mrow>
PiRepresent the active power of each node；QiRepresent the reactive power of each node；SimaxRepresent the apparent work(of each node Rate maximum；
3-6 logical variables constrain
To meet the feasibility of scheme implementation, there is following limitation to logical variable：
<mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;le;</mo> <msub> <mi>N</mi> <mrow> <mi>s</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mi>&amp;Omega;</mi> <mi>s</mi> <mi>u</mi> <mi>b</mi> </mrow> 3
<mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;le;</mo> <mn>1</mn> <mo>,</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mi>l</mi> <mi>f</mi> </mrow>
<mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;le;</mo> <mn>0</mn> <mo>,</mo> <mi>i</mi> <mo>&amp;Element;</mo> <mi>l</mi> <mi>e</mi> </mrow>
NsmaxRepresent that i transformer stations maximum can load the quantity of transformer, first formula limits transformer in a transformer station Quantity；Lf represents the set of default circuit in network, and le represents to have set up the set of circuit；Second and third formula limits The at most installation one of the feeder line of same position.
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Publication number Priority date Publication date Assignee Title
CN108306282A (en) * 2017-12-29 2018-07-20 国网宁夏电力有限公司经济技术研究院 It is a kind of with solve the problems, such as power grid diagnosis for be oriented to power distribution network automatic planning
CN109447498A (en) * 2018-11-08 2019-03-08 中南大学 A kind of Rail Transit System cost association multiple domain influent factor big data driving analysis method
CN109995026A (en) * 2019-03-22 2019-07-09 国网浙江省电力有限公司电力科学研究院 A kind of mixing alternating current-direct current Distribution network integration planning method based on genetic algorithm
CN110245799A (en) * 2019-06-18 2019-09-17 国网江西省电力有限公司经济技术研究院 Consider the multi-objective planning method of the Distribution Network Frame structural transition of load flexible demand

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CN108306282A (en) * 2017-12-29 2018-07-20 国网宁夏电力有限公司经济技术研究院 It is a kind of with solve the problems, such as power grid diagnosis for be oriented to power distribution network automatic planning
CN108306282B (en) * 2017-12-29 2021-05-14 国网宁夏电力有限公司经济技术研究院 Power distribution network automatic planning method with power grid diagnosis problem solving as guide
CN109447498A (en) * 2018-11-08 2019-03-08 中南大学 A kind of Rail Transit System cost association multiple domain influent factor big data driving analysis method
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CN109995026A (en) * 2019-03-22 2019-07-09 国网浙江省电力有限公司电力科学研究院 A kind of mixing alternating current-direct current Distribution network integration planning method based on genetic algorithm
CN110245799A (en) * 2019-06-18 2019-09-17 国网江西省电力有限公司经济技术研究院 Consider the multi-objective planning method of the Distribution Network Frame structural transition of load flexible demand

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