CN105550790B - Interconnected network idle work optimization calculation method based on non-topological approach equivalence - Google Patents
Interconnected network idle work optimization calculation method based on non-topological approach equivalence Download PDFInfo
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Abstract
The invention discloses a kind of interconnected network idle work optimization calculation methods based on non-topological approach equivalence, utilize computer, pass through program, first input the data such as voltage, the power at boundary node, external network equivalent network parameter is solved according to non-topological equivalent method, then the idle work optimization model for establishing interconnected network carries out idle work optimization calculating using interior point method.The more comprehensive information of outer net, by considering the comprehensive external network equivalent method of element, can be retained in equivalent network, to improve the precision of idle work optimization when outer net real-time synchronization data can not be obtained by the method for the present invention.The method of the present invention retains the power transfer relationship between boundary node and can accurately reflect outer net to the voltage power-less enabling capabilities of Intranet, to ensure that the precision that idle work optimization calculates by the comprehensive external network equivalent network of element of building.
Description
Technical field
The invention belongs to reactive power optimization of power system calculating fields, and in particular to interconnected network is without the whole network real-time synchronization data
Idle work optimization calculation method.
Background technique
With greatly developing for new energy, for the reasonable disposition of resource, it is tight that modern power systems have evolved into each subnet
Close to interconnect complicated big system, interaction and influence between each subnet also further enhance.Stable state point is carried out in each Intranet
It is necessary to consider the influence of closely coupled to it adjoining subnetworks when analysis decision.In order to guarantee that the idle work optimization of interconnected network calculates
Accuracy necessary consider influence of the outer net to Intranet.But it since outer net data volume is huge, is not easy in line computation and storage
Deposit, it is possible to external network equivalent is become with small scale, data are few, equivalent network easy to maintain and not concerning security matters, and then again into
Row idle work optimization calculates.But due to trade secret or mechanics of communication problem, it is difficult to the whole network real-time synchronization data are obtained, for this
Situation can carry out external network equivalent using non-topological approach, and then the idle work optimization for carrying out interconnected network calculates, it is ensured that idle
The accuracy of optimization.
The idle work optimization of existing interconnected network is mainly the Real-time Power Flow Information of known outer net network, if any the method for use
It is that Ward equivalence is carried out by the topological structure and operation data of outer net, the coordination strategy for then introducing idle work optimization carries out the whole network
Idle work optimization.The major defect of this method is if the whole network real-time synchronization data can not be obtained, and this method will be no longer applicable in.It is real
It also by external network equivalent is mostly PV at boundary node in the electric system of border, the major defect of this method: 1) PQ node cannot protect
Stay the power transfer relationship between boundary node.2) cannot accurately reflect outer net to the voltage power-less enabling capabilities of Intranet, no
It can guarantee the precision that idle work optimization calculates.
Summary of the invention
The purpose of the present invention is being directed to the deficiency of existing interconnected network idle work optimization, provide a kind of based on non-topological approach etc.
The interconnected network idle work optimization calculation method of value, this method utilize boundary in the case where that can not obtain outer net real-time synchronization data cases
Extranet information is carried out equivalent processing by the measurement information at node, and it is idle effectively to solve interconnected network under extranet information unknown situation
Optimize computational problem, while ensure that the accuracy that idle work optimization calculates.
Realizing the technical solution of the object of the invention is: a kind of interconnected network idle work optimization calculating based on non-topological approach equivalence
Method, by program, is first inputted under the method for operation of the voltage at boundary node, power and minimax using computer
Equivalent network supplemental characteristic solves external network equivalent network parameter according to non-topological equivalent method, then establishes the idle of interconnected network
Optimized model carries out idle work optimization calculating using interior point method.Specific step is as follows for the method:
1) m moment number is determined
PMU moment number needed for the determining solution equivalent network parameter of port number being connected according to intranet and extranet.
2mn > n2+6n (1)
N is the port number that intranet and extranet are connected in formula, and m is PMU sampling instant number to be asked.
2) input measurement data
Input the voltage measurements of PMU at m moment each boundary nodeWith m moment each side
The equivalent current measurements value that boundary's node is injected to IntranetWherein i=1,2 ..., n, n are intranet and extranet phase
Port number even, t=t1,t2,...,tm, t is PMU sampling instant, and m is total PMU sampling instant number.WithThere are m
Measured value.
3) equivalent network measurement equation is established
According to the voltage measurement and equivalent measurement of the 2) step input, the measurement equation of equivalent network is establishedWith
WithRespectively indicate the real part and imaginary part of measurement equation at i-th of boundary node of t moment.X=
[Ei,Re,Ei,Im,Zi,Re,Zi,Im,Zij,Re,Zij,Im,SLi,Re,SLi,Im,Bi]T, i=1,2 ..., n, j=1,2 ..., n, j ≠ i, x
For equivalent network parameter matrix to be asked, i represents i-th of boundary node, and j represents j-th of boundary node, and n is connected for intranet and extranet
Port number.Wherein Ei,ReAnd Ei,ImCorresponded at respectively i-th of boundary node equivalent virtual synchronous generator node voltage real part with
Imaginary part, Zi,ReAnd Zi,ImResistance and the reactance of equivalent branch, Z are corresponded at respectively i-th of boundary nodeij,ReAnd Zij,ImRespectively
The resistance of equivalent branch and reactance, S between i-th of boundary node and j-th of boundary nodeLi,ReAnd SLi,ImRespectively i-th
The real and imaginary parts of the corresponding equal currents of load at boundary node, BiIt is corresponding to ground leg at i-th of boundary node.WithThe voltage real and imaginary parts of respectively i-th boundary node, above formula t indicate t-th of moment,With
The voltage real and imaginary parts of respectively i-th boundary node.Ii,ReAnd Ii,ImThe equivalent electricity of load at respectively i-th of boundary node
The real and imaginary parts of the sum of the equivalent current that stream and boundary node are injected to Intranet.α and β are respectively representedReal part and
Imaginary part, η and μ are respectively representedReal and imaginary parts, wherein ZijBetween boundary node i and boundary node j etc.
It is worth impedance, ZikFor the equivalent impedance between boundary node i and boundary node k, k=1,2 ..., n, k ≠ i, j.
The above parameter can be detailed in attached drawing 1.
4) equivalent parameters constraint equation is established
Formula (4) is expressed as the equivalent parameters vector x of equivalent network under the maximum operational mode of inputmaxo:
xmaxo=[Ei,maxo,Ri,maxo,Xi,maxo,Rij,maxo,Xij,maxo,PLi,maxo,QLi,maxo,Bi,maxo]T (4)
Formula (5) is expressed as the equivalent parameters vector x of the equivalent network under the minimum operational mode of inputmino:
xmino=[Ei,mino,Ri,mino,Xi,mino,Rij,mino,Xij,mino,PLi,mino,QLi,mino,Bi,mino]T (5)
Formula (6)-(13) equivalent parameters constraint equation is established according to minimax method of operation equivalent parameters:
Bi,mino≤Bi'≤Bi,maxo (6)
Ri,maxo≤Zi,Re'≤Ri,mino (7)
Xi,maxo≤Zi,Im'≤Xi,mino (8)
Rij,maxo≤Zij,Re'≤Rij,mino (9)
Xij,maxo≤Zij,Im'≤Xij,mino (10)
PLi,mino≤SLi,Re'≤PLi,maxo (11)
QLi,mino≤SLi,Im'≤QLi,maxo (12)
Wherein Bi,minoAnd Bi,maxoI-th of boundary node institute is right respectively under minimum operational mode and under maximum operational mode
The equivalence answered is to ground leg, Bi' it is corresponding to ground leg at i-th of boundary node to be asked.Ri,minoAnd Ri,maxoRespectively
The resistance of equivalence branch corresponding to i-th of boundary node, Z under minimum operational mode and under maximum operational modei,Re' for currently to
The resistance of corresponding equivalence branch at i-th of the boundary node asked.Xi,minoAnd Xi,maxoIt is respectively under minimum operational mode and maximum
The reactance of equivalence branch corresponding to i-th of boundary node, Z under the method for operationi,Im' at i-th of boundary node currently to be asked
The reactance of corresponding equivalence branch.Rij,minoAnd Rij,maxoRespectively under minimum operational mode and maximum operational mode under i-th of boundary
The resistance of equivalent branch, Z between node and j-th of boundary nodeij,Re' it is i-th of boundary node currently to be asked and j-th of side
The resistance of equivalent branch between boundary's node.Xij,minoAnd Xij,maxoRespectively under minimum operational mode and i-th under maximum operational mode
The reactance of equivalent branch, Z between a boundary node and j-th of boundary nodeij,Im' for i-th of boundary node currently to be asked with
The reactance of equivalent branch between j-th of boundary node.Ei,minAnd Ei,maxRespectively under minimum operational mode and maximum operational mode
Equivalent virtual synchronous generator node voltage, E are corresponded at lower i-th of boundary nodei,Re' and Ei,Im' it is respectively i-th of side to be asked
Equivalent virtual synchronous generator node voltage real and imaginary parts are corresponded at boundary's node.PLi,minoAnd PLi,maxoRespectively minimum operation side
Load active power under formula and under maximum operational mode at i-th of boundary node, QLi,minoAnd QLi,maxoRespectively minimum operation
Reactive load power under mode and under maximum operational mode at i-th of boundary node, SLi,Re' and SLi,Im' it is respectively to be asked
The active power and reactive power of the corresponding duty value of load at i-th of boundary node.
5) Optimized model of equivalent network is established
Formula (14) is the objective function of equivalent network Optimized model, and m is PMU sampling instant number in formula, and n is connected for intranet and extranet
Port number.WithRespectively indicate the real part and imaginary part of measurement equation at i-th of boundary node of t moment.By formula
(6)-(14) constitute the Optimized model of equivalent network.
6) external network equivalent parameter is solved
Formula (6)-(14), which are constituted, solves external network equivalent nonlinearity in parameters optimization problem.It can directly be acquired by interior point method
External network equivalent parameter x.
7) objective function of idle work optimization is established
The least idle work optimization objective function of the whole network network loss is established based on the external network equivalent parameter sought in step 6):
min fI(QCI,QGI,KI,UGI,UGeq,QCeq,ULI,ULeq) (15)
F in formula (15)I(*) is the objective function of the whole network idle work optimization, QCIAnd QGIRespectively Intranet reactive power compensator is mended
The reactive power vector that the reactive power vector sum Intranet generator repaid issues；KIFor Intranet transformer voltage ratio vector；UGIAnd UGeq
Respectively Intranet generator terminal voltage vector sum external network equivalent generator terminal voltage vector；QGeqAnd QCeqIt is respectively equivalent outer
Reactive power vector of the net generator reactive power vector sum equivalence external network equivalent to ground leg；ULIAnd ULeqRespectively Intranet is non-
Generator node voltage vector sum equivalence outer net non-power generator node voltage vector.
8) equality constraint of idle work optimization is established
Establish the equality constraint of active power and reactive power respectively according to trend power balance equation:
In formula (16) and formula (17), a, b are Intranet and equivalent outer net node, a=1,2 ..., NA, b=1,2 ..., NA,
NAFor all node total numbers of Intranet and equivalent outer net；PaAnd QaRespectively the injection active power of node a and reactive power；Ua、
δaVoltage magnitude and phase angle at respectively node a, Ub、δbδ in voltage magnitude and phase angie type at respectively node ba,b=δa-
δb；Ga,b、Ba,bThe respectively real and imaginary parts of a row of node admittance matrix, b list element.Sin is respectively indicated with cos
SIN function and cosine function.
9) inequality constraints of idle work optimization is established
The inequality constraints of idle work optimization is established according to the bound of each control variable and state variable:
N in formula (18)-(26)CI,NGI,NKI,NLIAnd NBRespectively correspond Intranet reactive power compensator number of nodes, Intranet power generation
Machine number of nodes, Intranet transformer branch number, Intranet non-power generator number of nodes and boundary node number.At Intranet node c
Reactive power compensator compensation reactive power,QCIFor Intranet reactive power compensator compensation reactive power to
Amount,WithThe bound of reactive power compensator reactive power at respectively Intranet node c.At node d
The reactive power that Intranet generator issues,QGIFor Intranet generator issue reactive power vector,WithThe bound for the reactive power that generator issues at respectively Intranet node d.For e-th of transformer voltage ratio of Intranet,KIFor Intranet transformer voltage ratio vector,WithRespectively e-th of transformer voltage ratio bound of Intranet.For generator voltage amplitude at Intranet node d,UGIFor Intranet generator terminal voltage vector,
WithGenerator voltage amplitude bound at respectively Intranet node d.For the equivalent generator machine at outer net node g
Voltage magnitude is held, For external network equivalent generator terminal voltage vector,WithIt is respectively equivalent
Outer net generator voltage amplitude bound.For at outer net node g equivalent generator issue reactive power,QGeqFor equivalent outer net generator reactive power vector,WithRespectively equivalent outer net generator hair
Reactive power bound out.For the reactive power to ground leg equivalent at equivalent outer net node g,
QCeqIt is equivalent external network equivalent to the reactive power vector of ground leg,WithIt is equivalent at respectively equivalent outer net node g
To the reactive power bound of ground leg.For non-power generator node voltage amplitude at Intranet node l,ULIFor
Intranet non-power generator node voltage vector,WithAt respectively Intranet node l above and below non-power generator node voltage amplitude
Limit.For outer net non-power generator node voltage amplitude equivalent at node g,ULeqFor equivalent outer net non-power generating
Machine node voltage vector,WithEquivalent outer net non-power generator node voltage amplitude bound at respectively node g.
10) idle work optimization calculates
Convolution (15)-(26) can establish the idle work optimization computation model of interconnected network, solve the nothing by interior point method
Function Optimized model can calculate idle work optimization result.
After the present invention takes above-mentioned technical proposal, mainly have the following effects:
The method of the present invention can be when outer net real-time synchronization data can not obtain, by considering the comprehensive outer net etc. of element
Extranet information is retained and carries out idle work optimization by value method, improves precision.The method of the present invention is comprehensive outer by the element of building
Net equivalent network, the voltage that the power transfer relationship between boundary node can be retained and can accurately reflect outer net to Intranet
Reactive power support ability, to guarantee the precision that idle work optimization calculates.
Detailed description of the invention
Fig. 1 is the external network equivalent network for considering that element is comprehensive；
Fig. 2 is that IEEE39 node intranet and extranet divide figure.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples, but should not be construed the above-mentioned theme of the present invention
Range is only limitted to following embodiments.Without departing from the idea case in the present invention described above, known according to ordinary skill
Knowledge and customary means, make various replacements and change, should all include within the scope of the present invention.
IEEE39 node intranet and extranet as shown in Figure 2 divide figure, the interconnected network idle work optimization based on non-topological approach equivalence
Specific step is as follows for calculation method:
1) m moment number is determined
Number at the time of needed for the determining solution equivalent network parameter of port number being connected according to intranet and extranet.
2mn > n2+6n (1)
N=2 is the port number that intranet and extranet are connected in formula, and m is PMU sampling instant number to be asked.Calculated result: m > 4.In order to
Guarantee reduces calculation amount under the premise of having solution, takes m=5.
2) metric data is inputted
Input the voltage measurements of PMU at m=5 each moment boundary nodesIt is saved with each boundary
The equivalent current measurements value that point is injected to IntranetWherein i=1,2, n=2 are the end that intranet and extranet are connected
Mouth number, t=(t1,t2,...,t5), t is PMU sampling instant, and m=5 is total PMU sampling instant number.Wherein:
WithThere are 5 measured values.
3) equivalent network measurement equation is established
According to the voltage measurement and equivalent measurement of the 2) step input, the measurement equation of equivalent network is established.
WithRespectively indicate the real part and imaginary part of measurement equation at i-th of boundary node of t moment.X=
[Ei,Re,Ei,Im,Zi,Re,Zi,Im,Zij,Re,Zij,Im,SLi,Re,SLi,Im,Bi]T, i=1,2 ..., n, j=1,2 ..., n, j ≠ i, n
=2, i represent i-th of boundary node, and j represents j-th of boundary node, since there are many interstitial content, i=1, j=2 are taken to say here
Bright calculating process.X is equivalent network parameter matrix to be asked, wherein Ei,ReAnd Ei,ImIt is corresponded at respectively the 1st boundary node
Equivalent virtual synchronous generator node voltage real part and imaginary part, Zi,ReAnd Zi,ImEquivalent branch is corresponded at respectively the 1st boundary node
Resistance and reactance, Zij,ReAnd Zij,ImThe resistance of equivalent branch between respectively the 1st boundary node and the 2nd boundary node
And reactance, SLi,ReAnd SLi,ImThe real and imaginary parts of the corresponding equal currents of load at respectively the 1st boundary node, BiIt is
It is corresponding to ground leg at 1 boundary node.WithThe voltage real and imaginary parts of respectively the 1st boundary node, on
Formula t indicates t-th of moment, such as: work as t=t1When, then WithRespectively
The voltage real and imaginary parts of 2nd boundary node, whereinIi,ReAnd Ii,ImRespectively
The real and imaginary parts of the sum of the equivalent current injected for load equal currents and boundary node at the 1st boundary node to Intranet,
Ii,Re=3.0482, Ii,Im=-2.1872.α and β are respectively representedReal and imaginary parts, η and μ are respectively representedReal and imaginary parts.Wherein ZijFor the equivalent impedance between boundary node 1 and boundary node 2, ZikFor boundary node 1
With the equivalent impedance between boundary node k, k=(1,2), and because of k ≠ i, j, i.e. k ≠ 1,2, so under 2 port cases η and
μ is not present.
The above parameter can be detailed in attached drawing 1.The input value at 5 moment is brought into the measurement equation of 2 ports respectively respectively,
20 measurement equations can be obtained.
4) equivalent parameters constraint equation is established
Formula (4) is expressed as the equivalent parameters vector x of equivalent network under the maximum operational mode of inputmaxo；
xmaxo=[Ei,maxo,Ri,maxo,Xi,maxo,Rij,maxo,Xij,maxo,PLi,maxo,QLi,maxo,Bi,maxo]T (4)
Formula (5) is expressed as the equivalent parameters vector x of the equivalent network under the minimum operational mode of inputmino；
xmino=[Ei,mino,Ri,mino,Xi,mino,Rij,mino,Xij,mino,PLi,mino,QLi,mino,Bi,mino]T (5)
Formula (6)-(13) equivalent parameters constraint equation is established according to minimax method of operation equivalent parameters；
Bi,mino≤Bi'≤Bi,maxo (6)
Ri,maxo≤Zi,Re'≤Ri,mino (7)
Xi,maxo≤Zi,Im'≤Xi,mino (8)
Rij,maxo≤Zij,Re'≤Rij,mino (9)
Xij,maxo≤Zij,Im'≤Xij,mino (10)
PLi,mino≤SLi,Re'≤PLi,maxo (11)
QLi,mino≤SLi,Im'≤QLi,maxo (12)
Work as i=1, when j=2, illustrates calculating process.Wherein Bi,mino=0.7248 and Bi,maxo=1.0871 be respectively minimum
With equivalence corresponding to the 1st boundary node under maximum operational mode to ground leg, B under the method for operationi' it is currently to be asked the
It is corresponding to ground leg at 1 boundary node.Ri,mino=0.0055 and Ri,maxo=0.0018 is respectively under minimum operational mode
With the resistance of equivalence branch corresponding to the 1st boundary node under maximum operational mode, Zi,Re' it is the 1st boundary currently to be asked
The resistance of corresponding equivalence branch at node.Xi,mino=0.0054 and Xi,maxo=0.0016 be respectively minimum operational mode under and most
The reactance of equivalence branch corresponding to 1st boundary node, Z under the big method of operationi,Im' it is the 1st boundary node currently to be asked
The reactance of the corresponding equivalent branch in place.Rij,mino=0.0107 and Rij,maxo=0.0025 is respectively under minimum operational mode and maximum
Under the method for operation between the 1st boundary node and the 2nd boundary node equivalent branch resistance, Zij,Re' it is the currently to be asked the 1st
The resistance of equivalent branch between a boundary node and the 2nd boundary node.Xij,mino=0.1671 and Xij,maxo=0.0295 difference
For under minimum operational mode and under maximum operational mode between the 1st boundary node and the 2nd boundary node equivalent branch electricity
It is anti-, Zij,Im' between the 1st boundary node and the 2nd boundary node currently to be asked equivalent branch reactance.Ei,min=1.0
And Ei,max=1.1 be respectively under minimum operational mode and under maximum operational mode at the 1st boundary node a corresponding equivalence send out
Motor node voltage, Ei,Re' and Ei,Im' it is respectively that equivalent virtual synchronous generator node electricity is corresponded at the 1st boundary node to be asked
Press real and imaginary parts.PLi,mino=394.35Mw and PLi,maxo=693.34Mw is respectively to run under minimum operational mode with maximum
Load active power under mode at the 1st boundary node, QLi,mino=-1.95Mvar and QLi,maxo=14.49Mvar is respectively
Reactive load power under minimum operational mode and under maximum operational mode at the 1st boundary node, SLi,Re' and SLi,Im' respectively
For the active power and reactive power of the corresponding duty value of load at the 1st boundary node to be asked.
5) Optimized model of equivalent network is established
Formula (14) is the objective function of equivalent network Optimized model, and m=5 is PMU sampling instant number in formula, and n=2 is inside and outside
The connected port number of net.WithRespectively indicate the real part of measurement equation and void at i-th of boundary node of t moment
Portion.The Optimized model of equivalent network is constituted by formula (6)-(14).
6) external network equivalent parameter is solved
Formula (6)-(14), which are constituted, solves external network equivalent nonlinearity in parameters optimization problem.It can directly be acquired by interior point method
External network equivalent parameter x.
Calculated result: E1=1.0529 ∠ 0.1811, E2=1.0472 ∠ -0.8853, Z1,Re=0.0036, Z1,Im=
0.0373, Z2,Re=0.0035, Z2,Im=0.0490, Z12,Re=0.0066, Z12,Im=0.0943, SLI,Re=2.1501, SLI,Im
=-2.558, SL2,Re=2.3980, SL2,Im=0.7484, B1=0.9061, B2=0.8503.
7) objective function of idle work optimization is established
The least idle work optimization objective function of the whole network network loss is established based on the external network equivalent parameter sought in (6) step:
min fI(QCI,QGI,KI,UGI,UGeq,QCeq,ULI,ULeq) (15)
F in formula (15)I(*) is the objective function of the whole network idle work optimization, QCIAnd QGIRespectively Intranet reactive power compensator is mended
The reactive power vector that the reactive power vector sum Intranet generator repaid issues；KIFor Intranet transformer voltage ratio vector；UGIAnd UGeq
Respectively Intranet generator terminal voltage vector sum external network equivalent generator terminal voltage vector；QGeqAnd QCeqIt is respectively equivalent outer
Reactive power vector of the net generator reactive power vector sum equivalence external network equivalent to ground leg；ULIAnd ULeqRespectively Intranet is non-
Generator node voltage vector sum equivalence outer net non-power generator node voltage vector.
8) equality constraint of idle work optimization is established
Establish the equality constraint of active power and reactive power respectively according to trend power balance equation:
In formula (16) and formula (17), a (a=1,2 ..., NA) and b (b=1,2 ..., NA) it is Intranet and equivalent outer net section
Point, a can be equal to b, NAFor all node total numbers of Intranet and equivalent outer net；PaAnd QaThe respectively injection active power of node a
With reactive power, Ua、δaVoltage magnitude and phase angle at respectively node a, Ub、δbVoltage magnitude and phase at respectively node b
Angle, δ in formulaa,b=δa-δb；Ga,b、Ba,bThe respectively real and imaginary parts of a row of node admittance matrix, b list element.sin
SIN function and cosine function are respectively indicated with cos.
9) inequality constraints of idle work optimization is established
The inequality constraints of idle work optimization is established according to the bound of each control variable and state variable:
N in formula (18)-(26)CI=1, NGI=6, NKI=9, NLI=20 and NB=2 respectively correspond Intranet reactive power compensator
Number of nodes, Intranet generator number of nodes, Intranet transformer branch number, Intranet non-power generator number of nodes and boundary node number.By
It is too many in number of nodes, take 1 type node to illustrate that inequality constraints condition building process, i.e. hypothesis c, d, e, g, l are equal respectively
It is 1.For the reactive power compensator reactive power at Intranet node c,QCIFor Intranet reactive power compensator benefit
The reactive power vector repaid,WithReactive power compensator at respectively Intranet node c without
The bound of function power.For at node d Intranet generator issue reactive power,QGIFor Intranet power generation
The reactive power vector that machine issues,WithGenerator is sent out at respectively Intranet node d
The bound of reactive power out.For e-th of transformer voltage ratio of Intranet,KIFor Intranet transformer voltage ratio vector,WithRespectively e-th of transformer voltage ratio bound of Intranet；For generator end at Intranet node d
Voltage magnitude,UGIFor Intranet generator terminal voltage vector,WithRespectively
Generator voltage amplitude bound at Intranet node d.For the equivalent generator terminal voltage amplitude at outer net node g,UGeqFor external network equivalent generator terminal voltage vector,WithIt is respectively equivalent
Outer net generator voltage amplitude bound.For at outer net node g equivalent generator issue reactive power,QGeqFor equivalent outer net generator reactive power vector,WithPoint
It Wei not the reactive power bound that issues of equivalent outer net generator.For the nothing to ground leg equivalent at equivalent outer net node g
Function power,QCeqIt is equivalent external network equivalent to the reactive power vector of ground leg,
WithThe equivalent reactive power bound to ground leg at respectively equivalent outer net node g.It is interior
Non-power generator node voltage amplitude at net node l,ULIFor Intranet non-power generator node voltage vector,WithNon-power generator node voltage amplitude bound at respectively Intranet node l.For node
Equivalent outer net non-power generator node voltage amplitude at g,ULeqFor equivalent outer net non-power generator node voltage vector,WithEquivalent outer net non-power generator node voltage amplitude bound at respectively node g.
10) idle work optimization calculates
Convolution (15)-(26) can establish the idle work optimization computation model of interconnected network, solve the nothing by interior point method
Function Optimized model can calculate idle work optimization result.
Calculated result: QG31=497.13Mvar, QG32=359.93Mvar, QG33=174.59Mvar, QG34=
140.66Mvar, QG35=293.31Mvar, QG36=139.77Mvar.
Test result
The method of the present invention is hung using the interconnected network idle work optimization calculation method based on non-topological approach equivalence and using outer net
Equal check-ins idle work optimization method compares, i.e., PQ equivalence and PV are equivalent, by carrying out idle work optimization calculated result with the whole network
Relative error and absolute error compare.Relative error and absolute error is smaller illustrates that this method effect is better.It can be in table 1
Find out the relative error of the method for the present invention and absolute error be it is the smallest, so as to judge the validity of the method for the present invention.
The generator reactive power output error result of the different equivalence method idle work optimizations of table 1
In table 1 it can be seen that the relative error and absolute error of the method for the present invention be it is the smallest, so as to judge this
The validity of inventive method.
From the experimental results:
The method of the present invention can be when outer net real-time synchronization data can not obtain, by considering the comprehensive outer net etc. of element
The more comprehensive information of outer net is retained in equivalent network, to improve the precision of idle work optimization by value method.
The method of the present invention retains the power transfer between boundary node by the comprehensive external network equivalent network of element of building
Relationship and can accurately reflect outer net to the voltage power-less enabling capabilities of Intranet, thus ensure that idle work optimization calculate essence
Degree.
Claims (1)
1. the interconnected network idle work optimization calculation method based on non-topological approach equivalence, it is characterised in that: the method specific steps
Including the following contents；
1) m moment number is determined
According to the port number that intranet and extranet are connected, PMU moment number needed for solving equivalent network parameter is determined by formula (1)；
2mn > n2+6n (1)
In formula, n is the port number that intranet and extranet are connected, and m is total PMU sampling instant number；
2) input measurement data
Input the voltage measurements of PMU at m moment each boundary nodeWith m moment each boundary section
The equivalent current measurements value that point is injected to IntranetWherein i=1,2 ..., n, n are what intranet and extranet were connected
Port number, t=t1, t2..., tm, t is PMU sampling instant, and m is total PMU sampling instant number；
3) equivalent network measurement equation is established
According to the voltage measurement and equivalent measurement of the 2) step input, the measurement equation of equivalent network is establishedWith
WithRespectively indicate the real part and imaginary part of measurement equation at i-th of boundary node of t moment, x=[EI, Re,
EI, Im, ZI, Re, ZI, Im, ZIj, Re, ZIj, Im, SLi, Re, SLi, Im, Bi]T, i=1,2 ..., n, j=1,2 ..., n, j ≠ i, x are wait ask
Equivalent network parameter matrix, i represents i-th of boundary node, and j represents j-th of boundary node, and n is the port that intranet and extranet are connected
Number；Wherein EI, ReAnd EI, ImEquivalent virtual synchronous generator node voltage real part and imaginary part are corresponded at respectively i-th of boundary node；
ZI, ReAnd ZI, ImResistance and the reactance of equivalent branch are corresponded at respectively i-th of boundary node；ZIj, ReAnd ZIj, ImRespectively i-th
The resistance of equivalent branch and reactance between a boundary node and j-th of boundary node；SLi, ReAnd SLi, ImRespectively i-th of boundary
The real and imaginary parts of the corresponding equal currents of load at node；BiIt is corresponding to ground leg at i-th of boundary node；
WithThe voltage real and imaginary parts of respectively i-th boundary node；WithThe voltage of respectively j-th boundary node
Real and imaginary parts, t are PMU sampling instant；II, ReAnd II, ImLoad equal currents and boundary are saved at respectively i-th of boundary node
The real and imaginary parts of the sum of the equivalent current that point is injected to Intranet；α and β are respectively representedReal and imaginary parts, η and μ
It respectively representsReal and imaginary parts, wherein ZijFor the equivalent impedance between boundary node i and boundary node j, Zik
For the equivalent impedance between boundary node i and boundary node k, k=1,2 ..., n, k ≠ i, j；
4) equivalent parameters constraint equation is established
Formula (4) is expressed as the equivalent parameters vector x of equivalent network under the maximum operational mode of inputmaxo；
xmaxo=[EI, maxo, RI, maxo, XI, maxo, RIj, maxo, XIj, maxo, PLi, maxo, QLi, maxo, BI, maxo]T (4)
Formula (5) is expressed as the equivalent parameters vector x of the equivalent network under the minimum operational mode of inputmino；
xmino=[EI, mino, RI, mino, XI, mino, RIj, mino, XIj, mino, PLi, mino, QLi, mino, BI, mino]T] (5)
Formula (6)-(13) equivalent parameters constraint equation is established according to minimax method of operation equivalent parameters；
BI, mino≤Bi'≤BI, maxo (6)
RI, maxo≤ZI, Re'≤RI, mino (7)
XI, maxo≤ZI, Im'≤XI, mino (8)
RIj, maxo≤Zij, Re'≤RIj, mino (9)
XIj, maxo≤ZIj, Im'≤XIj, mino (10)
PLi, mino≤SLi, Re'≤PLi, maxo (11)
QLi, mino≤SLi, Im'≤QLi, maxo (12)
Wherein BI, minoAnd BI, maxoRespectively under minimum operational mode and corresponding to i-th of boundary node under maximum operational mode
Equivalence is to ground leg；Bi' it is corresponding to ground leg at i-th of boundary node currently to be asked；RI, minoAnd RI, maxoRespectively
The resistance of equivalence branch corresponding to i-th of boundary node under minimum operational mode and under maximum operational mode；ZI, Re' for currently to
The resistance of corresponding equivalence branch at i-th of the boundary node asked；XI, minoAnd XI, maxoIt is respectively under minimum operational mode and maximum
The reactance of equivalence branch corresponding to i-th of boundary node under the method for operation；ZI, Im' at i-th of boundary node currently to be asked
The reactance of corresponding equivalence branch；RIj, minoAnd RIj, maxoRespectively under minimum operational mode and maximum operational mode under i-th of boundary
The resistance of equivalent branch between node and j-th of boundary node；ZIj, Re' it is i-th of boundary node currently to be asked and j-th of side
The resistance of equivalent branch between boundary's node；XIj, minoAnd XIj, maxoRespectively under minimum operational mode and i-th under maximum operational mode
The reactance of equivalent branch between a boundary node and j-th of boundary node；ZIj, Im' for i-th of boundary node currently to be asked with
The reactance of equivalent branch between j-th of boundary node；EI, minoAnd EI, maxoRespectively under minimum operational mode and maximum operation side
Equivalent virtual synchronous generator node voltage is corresponded under formula at i-th of boundary node；EI, Re' and EI, Im' it is respectively i-th to be asked
Equivalent virtual synchronous generator node voltage real and imaginary parts are corresponded at boundary node；PLi, minoAnd PLi, maxoRespectively minimum operation
Load active power under mode and under maximum operational mode at i-th of boundary node；QLi, minoAnd QLi, maxoRespectively minimum fortune
Reactive load power under line mode and under maximum operational mode at i-th of boundary node；SLi, Re' and SLi, Im' it is respectively wait ask
I-th of boundary node at the corresponding duty value of load active power and reactive power；
5) Optimized model of equivalent network is established
The objective function of equivalent network Optimized model is established using formula (14)；
M is total PMU sampling instant number in formula, and n is the port number that intranet and extranet are connected；WithRespectively indicate t moment
The real part and imaginary part of measurement equation at i boundary node；
6) external network equivalent parameter is solved
External network equivalent parameter x is directly acquired by interior point method；
7) objective function of idle work optimization is established
The least idle work optimization objective function of the whole network network loss is established based on the external network equivalent parameter sought in step 6)；
minfI(QCI, QGI, KI, UGI, UGeq, QGeq, QCeq, ULI, ULeq) (15)
F in formula (15)I(*) is the objective function of the whole network idle work optimization；QCIAnd QGIRespectively Intranet reactive power compensator compensates
The reactive power vector that reactive power vector and Intranet generator issue；KIFor Intranet transformer voltage ratio vector；UGIAnd UGeqRespectively
For Intranet generator terminal voltage vector sum external network equivalent generator terminal voltage vector；QGeqAnd QCeqRespectively equivalent outer net hair
Reactive power vector of the motor reactive power vector sum equivalence external network equivalent to ground leg；ULIAnd ULeqRespectively Intranet and equivalence
Outer net non-power generator node voltage vector；
8) equality constraint of idle work optimization is established
Establish the equality constraint of active power and reactive power respectively according to trend power balance equation；
In formula (16) and (17), a, b are Intranet and equivalent outer net node, a=1,2 ..., NA, b=1,2 ..., NA, NAIt is interior
All node total numbers of net and equivalent outer net, PaAnd QaRespectively the injection active power of node a and reactive power, Ua、δaRespectively
For the voltage magnitude and phase angle at node a, Ub、δbVoltage magnitude and phase angle at respectively node b, δ in formulaa,b=δa-δb；
Ga,b、Ba,bThe respectively real and imaginary parts of a row of node admittance matrix, b list element, sin and cos respectively indicate sine
Function and cosine function；
9) inequality constraints of idle work optimization is established
The inequality constraints of idle work optimization is established according to the bound of each control variable and state variable:
N in formula (18)-(26)CI, NGI, NKI, NLIAnd NBRespectively correspond Intranet reactive power compensator number of nodes, Intranet generator section
Points, Intranet transformer branch number, Intranet non-power generator number of nodes and boundary node number；QCIcIt is idle at Intranet node c
The reactive power of compensation device compensation, QCIc∈QCI, QCIFor Intranet reactive power compensator compensation reactive power vector,WithThe bound of reactive power compensator reactive power at respectively Intranet node c；For the Intranet generator at node d
The reactive power of sending,QGIFor Intranet generator issue reactive power vector,WithIn respectively
The bound for the reactive power that generator issues at net node d；For e-th of transformer voltage ratio of Intranet,KIIt is interior
Net transformer voltage ratio vector,WithRespectively e-th of transformer voltage ratio bound of Intranet；To be sent out at Intranet node
Motor terminal voltage amplitude,UGIFor Intranet generator terminal voltage vector,WithRespectively Intranet node d
Locate generator voltage amplitude bound；For the equivalent generator terminal voltage amplitude at outer net node g,UGeqFor external network equivalent generator terminal voltage vector,WithRespectively equivalent outer net generator end
Voltage magnitude bound；For at outer net node g equivalent generator issue reactive power,QGeqFor etc.
It is worth outer net generator reactive power vector,WithThe reactive power bound that respectively equivalent outer net generator issues；For the reactive power to ground leg equivalent at equivalent outer net node g,QCeqOver the ground for equivalent external network equivalent
The reactive power vector of branch,WithThe respectively equivalent place outer net node g it is equivalent to the reactive power of ground leg above and below
Boundary；For non-power generator node voltage amplitude at Intranet node l,ULIFor Intranet non-power generator node voltage to
Amount,WithNon-power generator node voltage amplitude bound at respectively Intranet node l；It is equivalent outer at node g
Net non-power generator node voltage amplitude,ULeqFor equivalent outer net non-power generator node voltage vector,WithEquivalent outer net non-power generator node voltage amplitude bound at respectively node g；
10) idle work optimization calculates
The idle work optimization computation model of interconnected network is established in convolution (15)-(26), solves the idle work optimization mould by interior point method
Type calculates idle work optimization result.
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