CN108764738B - Urban power transmission network safety probability assessment method considering elasticity margin - Google Patents

Urban power transmission network safety probability assessment method considering elasticity margin Download PDF

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CN108764738B
CN108764738B CN201810553664.9A CN201810553664A CN108764738B CN 108764738 B CN108764738 B CN 108764738B CN 201810553664 A CN201810553664 A CN 201810553664A CN 108764738 B CN108764738 B CN 108764738B
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吕林
杨昕然
许立雄
刘友波
姚一杨
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State Grid Zhejiang Electric Power Co Ltd
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Abstract

The invention relates to an urban power transmission network safety probability assessment method considering elasticity margin. In the invention, a wind power plant output power probability model and a comprehensive load power demand probability model are used for describing the change of the injection power of the nodes of the power transmission network; the three-point estimation method is used for selecting the evaluation samples to form a sample evaluation matrix, so that the evaluation calculation amount is reduced; the node injection power change causes the power flow of each branch circuit to deviate in different degrees, the branch circuits sensitive to the power fluctuation of certain nodes can deviate in larger power flow, and the RSSD can reflect the sensitivity degree of the safety of the power transmission network to the power change of the node; each sample in the sample evaluation matrix corresponds to the determined node injection power, the high-voltage distribution network is reconstructed to change the operation mode through load transfer so that the transmission network generates an elastic margin, and a feasible topological state of the high-voltage distribution network is selected as the operation mode so that each evaluation sample has the maximum safety margin.

Description

Urban power transmission network safety probability assessment method considering elasticity margin
Technical Field
The invention relates to the field of urban power grid safety assessment, in particular to an urban power transmission grid safety probability assessment method considering elasticity margin.
Background
The gradual increase of the permeability of the distributed power supply and the electric automobile in the power grid makes the load space-time distribution imbalance more severe. The high-voltage distribution network (110kV) is used as a transition power grid of an urban power transmission network (220kV) and a medium-voltage distribution network (10kV or below), is a key link for ensuring the urban power supply quality and safety, has a flexible topological structure, has a large number of standby supply lines, can realize the great change of the operation mode by switching the states of the main and standby supply paths, and leads the power flow distribution of the power transmission network. The transmission line is used as an important carrier for transmitting electric energy, and the transmission safety of the transmission line cannot be ignored for the operation safety of the transmission network. At present, the transmission safety margin indexes are only analyzed on the researched lines in an isolated mode, the lines are not related to the topological positions of the lines, the influences of power output and load fluctuation on the safety of branch circuits cannot be taken into consideration, and the safety margin of a power transmission network cannot be directly embodied by the safety of a certain branch circuit.
Disclosure of Invention
The invention aims to solve the technical problem of providing an urban power transmission network safety probability assessment method considering elastic margin, and solving the problem of inaccurate calculation of the power transmission network safety margin.
The technical scheme for solving the technical problems is as follows: a safety probability assessment method for an urban power transmission network considering elasticity margin comprises the following steps:
s1, initializing structures, element parameters and node injection power probability models of the power grid and the high-voltage distribution network;
s2, selecting estimation points of random variables in the node injection power probability model through the principle of a three-point estimation method to form a sample evaluation matrix Xr；
S3, sample matrix XrCalculating an evaluation index value of the power grid safety margin and a corresponding weight coefficient of the evaluation index value by each evaluation sample;
s4, when the evaluation index values of all the evaluation samples and the corresponding weight coefficients are obtained, the step S5 is executed, otherwise, the step S3 is executed;
and S5, calculating a v-order origin moment of each evaluation sample evaluation index value through the weight coefficient, and expanding the v-order origin moment by utilizing a Cornish-fisher series to obtain the safety probability distribution of the power transmission network.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, the specific steps of calculating the node injection power probability model in step S1 are as follows:
s11, calculating the output power P of the wind powerwindThe calculation formula is as follows:
Figure GDA0003331556130000021
in the formula (1), v is the wind speed, vciFor cutting into the wind speed, vrRated wind speed, vcoFor cutting out the wind speed, PrIs the rated power of the wind turbine generator,
Figure GDA0003331556130000022
s12, calculating a wind power plant output power probability model f (P)wind) The calculation formula is as follows:
Figure GDA0003331556130000023
in the formula (2), K is a Weibull distribution shape parameter, and C is a scale parameter;
s13, calculating a probability model of the comprehensive load power demand of the node at the time t, wherein the calculation formula is as follows:
Figure GDA0003331556130000024
in the formula (3), μP,t、σP,tRespectively, the active expected value and standard deviation, P, of the integrated node load at time tLFor integrated load active power demand, muCLQ,tFor normal load reactive expectation, σCLQ,tFor normal load reactive standard deviation, QLThe reactive power requirement of the comprehensive load is met.
Further, the step S3 includes the following specific steps:
s31, calculating the safety margin RSSD of the transmission grid branch iiThe calculation formula is as follows:
Figure GDA0003331556130000031
in the formula (4), PimaxIs the maximum transmission capacity, P, of branch iiIs the current transmission power, σ, of branch iG-iContributing factor G to branch i for each power supplym-iStandard deviation of (a)L-iContributing factor G to branch i for each node loadn-iStandard deviation of (d);
wherein each power supply contributes a factor G to branch im-iThe calculation formula of (2) is as follows:
Figure GDA0003331556130000032
in the formula (5), Δ PiIs the active output variation, Δ P, of branch iGmIs the active output variation, X, of the node m power supplyiIs the reactance of branch i, l, k are the first and last nodes of branch i, Xlm、XkmRespectively an l row and m columns and a k row and m columns in the reactance matrix;
each node load contributes factor G to branch in-iThe calculation formula of (2) is as follows:
Figure GDA0003331556130000033
in the formula (6), Δ PLnFor the variation of the load of node n, Xln、XknRespectively an n column in the l row and an n column in the k row in the reactance matrix;
s32, calculating an evaluation index value RSSD of the power grid safety margin, wherein the calculation formula is as follows:
RSSD＝min(RSSDi)i∈SL (7)
in the formula (7), SLIs a set containing all branches.
S33, maximizing an evaluation index value RSSD of the power grid safety margin through topology reconstruction of the high-voltage power distribution network, and constructing an optimization model, wherein the optimization model comprises a target function and constraint conditions;
the objective function is:
f＝max RSSD (8)
the alternating current power flow constraint under the ith topological structure is as follows:
Figure GDA0003331556130000041
in the formula (9), the reaction mixture is,
Figure GDA0003331556130000042
respectively the active and reactive power of the wind farm at node j,
Figure GDA0003331556130000043
respectively the active demand and the reactive demand of the load at node j,
Figure GDA0003331556130000044
is the voltage at node k connected to node j,
Figure GDA0003331556130000045
is the voltage at the node j and,
Figure GDA0003331556130000046
to connect the conductances of the nodes k and j legs,
Figure GDA0003331556130000047
is the voltage phase difference of nodes k and j,
Figure GDA0003331556130000048
susceptance for connecting the branches k and j;
wherein the active demand of the load at node j
Figure GDA0003331556130000049
The calculation formula of (2) is as follows:
Figure GDA00033315561300000410
in the formula (10), the first and second groups,
Figure GDA00033315561300000411
to reconstruct the active load at the front node j,
Figure GDA00033315561300000412
the active load transferred at the node j under the ith topological structure after reconstruction;
reactive demand of load at node j
Figure GDA00033315561300000413
The calculation formula of (2) is as follows:
Figure GDA00033315561300000414
in the formula (11), the reaction mixture is,
Figure GDA00033315561300000415
to reconstruct the reactive load at node j before,
Figure GDA00033315561300000416
the reactive load transferred at the node j under the ith topological structure after reconstruction;
the section power constraint under the ith topological structure is as follows:
Figure GDA00033315561300000417
in the formula (12), the first and second groups,
Figure GDA00033315561300000418
for the active power transmitted on the n-th section connecting line,
Figure GDA00033315561300000419
is the setting value of the active power of the nth section, Slink,nSet of links included in the nth cross-section, NcutThe number of the sections;
the upper and lower limits of the active and reactive output power of the wind power under the ith topological structure are constrained as follows:
Figure GDA00033315561300000420
in the formula (13), the first and second groups,
Figure GDA00033315561300000421
the lower limit of the wind power active output power at the node j is defined,
Figure GDA00033315561300000422
the upper limit of the wind power active output power at the node j is defined,
Figure GDA00033315561300000423
is the lower limit of the wind power reactive output power at the node j,
Figure GDA00033315561300000424
the upper limit of the wind power reactive output power at the node j is set;
the node voltage constraint under the ith topology is as follows:
Figure GDA0003331556130000051
in the formula (14), VminIs the lower limit of the node voltage, VmaxIs the upper limit of the node voltage;
the branch power constraint under the ith topology is as follows:
Figure GDA0003331556130000052
in the formula (15), the first and second groups,
Figure GDA0003331556130000053
the branch connecting nodes k and j transmits power,
Figure GDA0003331556130000054
for the lower limit of the branch transmission power connecting nodes k and j,
Figure GDA0003331556130000055
transmitting an upper limit of power for a branch connecting nodes k and j;
reconstruction time distribution unit group DwAnd (3) limiting the switching times:
0≤Dw≤Dw,max (16)
in the formula (16), Dw,maxAs a unit group DwMaximum number of switching actions;
s34, adding a wind power plant output power probability model and a node comprehensive load power demand probability model into the optimization model to form a nonlinear model between the safety margin of the power transmission network and the injection power of each node:
F＝h(X) (17)
in equation (17), h () is a nonlinear function of the injected power of each node and the grid safety margin, X is a random vector for the injected power of each node, and X ═ X1,X2,…,Xm]；
S35, obtaining an evaluation index value RSSD by solving the nonlinear model;
s36, calculating output power and comprehensive load demand X of wind power plantiIs sampled byi,k：
xi,k＝μi+ξi,kσi，k＝1,2,3 (18)
In the formula (18), μi、σiAre respectively variable XiMean and standard deviation ofi,kIs a sample value xi,kThe position coefficient of (a);
wherein the position coefficient xii,kThe calculation formula of (2) is as follows:
Figure GDA0003331556130000056
s37, passing position coefficient xii,kCalculating a weight coefficient omegai,k：
Figure GDA0003331556130000061
In the formula (20), λi,3And λi,4Are respectively variable XiSkewness and kurtosis ofi,1And xii,2Are respectively variable XiM is the number of nodes with injected power.
The invention has the beneficial effects that: in the invention, a wind power plant output power probability model and a comprehensive load power demand probability model are used for describing the change of the injection power of the nodes of the power transmission network; the three-point estimation method is used for selecting the evaluation samples to form a sample evaluation matrix, so that the evaluation calculation amount is reduced; the evaluation index RSSD is used for connecting the safety margin of the branch circuit with the network topology structure, so that the safety margin of the power transmission network is determined by the branch circuit of the 'short board', and the RSSD can reflect the influence of the node injection power change on the safety margin of the power transmission network; the node injection power change causes the power flow of each branch circuit to deviate in different degrees, the branch circuits sensitive to the power fluctuation of certain nodes can deviate in larger power flow, and the RSSD can reflect the sensitivity degree of the safety of the power transmission network to the power change of the node; each sample in the sample evaluation matrix corresponds to the determined node injection power, the high-voltage distribution network is reconstructed to change the operation mode through load transfer so that the transmission network generates an elastic margin, and a feasible topological state of the high-voltage distribution network is selected as the operation mode so that each evaluation sample has the maximum safety margin.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a flowchart of the method for computing a node injection power probability model in step S1 according to the present invention;
FIG. 3 is a flowchart of step S3 according to the present invention;
FIG. 4 is a schematic diagram of a scenario of the present invention;
FIG. 5 is a schematic diagram of a grid security domain and safety margin in accordance with the present invention;
fig. 6 is a schematic diagram of the elasticity margin of the power grid after the high-voltage distribution network is reconstructed according to the invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1, a method for evaluating safety probability of an urban power transmission network considering elasticity margin includes the following steps:
s1, initializing structures, element parameters and node injection power probability models of the power grid and the high-voltage distribution network;
s2, selecting estimation points of random variables in the node injection power probability model through the principle of a three-point estimation method to form a sample evaluation matrix Xr；
S3, sample matrix XrCalculating an evaluation index value of the power grid safety margin and a corresponding weight coefficient of the evaluation index value by each evaluation sample;
s4, when the evaluation index values of all the evaluation samples and the corresponding weight coefficients are obtained, the step S5 is executed, otherwise, the step S3 is executed;
and S5, calculating a v-order origin moment of each evaluation sample evaluation index value through the weight coefficient, and expanding the v-order origin moment by utilizing a Cornish-fisher series to obtain the safety probability distribution of the power transmission network.
As shown in fig. 2, the specific steps of calculating the node injection power probability model in step S1 are as follows:
s11, calculating the output power P of the wind powerwindThe calculation formula is as follows:
Figure GDA0003331556130000071
in the formula (1), v is the wind speed, vciFor cutting into the wind speed, vrRated wind speed, vcoFor cutting out the wind speed, PrIs the rated power of the wind turbine generator,
Figure GDA0003331556130000072
s12, calculating a wind power plant output power probability model f (P)wind) The calculation formula is as follows:
Figure GDA0003331556130000073
in the formula (2), K is a Weibull distribution shape parameter, and C is a scale parameter;
calculating the node load P at the moment tLDThe calculation formula is as follows:
PLD＝atPCL+(1-at)PEV (21)
in the formula (21), atIs a time-varying coefficient at time t, PCLFor normal loading, PEVCharging a load for the electric vehicle;
calculating charging load P of electric automobileEVAnd normal load PCLThe calculation formula is as follows:
Figure GDA0003331556130000081
Figure GDA0003331556130000082
in the formula (22) and the formula (23), ft(PEV) Charging load P for electric vehicleEVDistribution characteristic of (f)t(PCL) Is a normal load PCLDistribution characteristic of (f)t(QCL) For the distribution characteristics of reactive power of a conventional load, muEV,tAnd λEV,tRespectively the expected value and the coefficient of variation, mu, of the charging load of the electric vehicleCLP,t、μCLQ,t、σCLP,tAnd σCLQ,tRespectively the active expected value, the active standard deviation, the reactive expected value and the reactive standard deviation of the conventional load
S13, calculating a probability model of the comprehensive load power demand of the node at the time t, wherein the calculation formula is as follows:
Figure GDA0003331556130000083
in the formula (3), μPt、σPtRespectively, the active expected value and standard deviation, P, of the integrated node load at time tLFor integrated load active power demand, muCLQtFor normal load reactive power desired value, σCLQtFor normal load reactive power standard deviation, QLThe reactive power requirement of the comprehensive load is met.
As shown in fig. 3, the specific steps of step S3 are:
s31, calculating the safety margin RSSD of the transmission grid branch iiThe calculation formula is as follows:
Figure GDA0003331556130000084
in the formula (4), PimaxIs the maximum transmission capacity, P, of branch iiIs the current transmission power, σ, of branch iG-iContributing factor G to branch i for each power supplym-iStandard deviation of (a)L-iContributing factor G to branch i for each node loadn-iStandard deviation of (d);
wherein each power supply contributes a factor G to branch im-iThe calculation formula of (2) is as follows:
Figure GDA0003331556130000091
in the formula (5), Δ PiIs the active output variation, Δ P, of branch iGmIs the active output variation, X, of the node m power supplyiIs the reactance of branch i, l, k are the first and last nodes of branch i, Xlm、XkmRespectively an l row and m columns and a k row and m columns in the reactance matrix;
each node load contributes factor G to branch in-iThe calculation formula of (2) is as follows:
Figure GDA0003331556130000092
in the formula (6), Δ PLnFor the variation of the load of node n, Xln、XknRespectively an n column in the l row and an n column in the k row in the reactance matrix;
s32, calculating an evaluation index value RSSD of the power grid safety margin, wherein the calculation formula is as follows:
RSSD＝min(RSSDi)i∈SL (7)
in the formula (7), SLIs a set containing all branches.
S33, maximizing an evaluation index value RSSD of the power grid safety margin through topology reconstruction of the high-voltage power distribution network, and constructing an optimization model, wherein the optimization model comprises a target function and constraint conditions;
the objective function is:
f＝max RSSD (8)
the alternating current power flow constraint under the ith topological structure is as follows:
Figure GDA0003331556130000093
in the formula (9), the reaction mixture,
Figure GDA0003331556130000094
respectively the active and reactive power of the wind farm at node j,
Figure GDA0003331556130000095
respectively the active demand and the reactive demand of the load at node j,
Figure GDA0003331556130000096
is the voltage at node k connected to node j,
Figure GDA0003331556130000101
is the voltage at the node j and,
Figure GDA0003331556130000102
to connect the conductances of the nodes k and j legs,
Figure GDA0003331556130000103
is the voltage phase difference of nodes k and j,
Figure GDA0003331556130000104
susceptance for connecting the branches k and j;
wherein the active demand of the load at node j
Figure GDA0003331556130000105
The calculation formula of (2) is as follows:
Figure GDA0003331556130000106
in the formula (10), the first and second groups,
Figure GDA0003331556130000107
to reconstruct the active load at the front node j,
Figure GDA0003331556130000108
the active load transferred at the node j under the ith topological structure after reconstruction;
reactive demand of load at node j
Figure GDA0003331556130000109
The calculation formula of (2) is as follows:
Figure GDA00033315561300001010
in the formula (11), the reaction mixture,
Figure GDA00033315561300001011
to reconstruct the reactive load at node j before,
Figure GDA00033315561300001012
the reactive load transferred at the node j under the ith topological structure after reconstruction;
the section power constraint under the ith topology is as follows:
Figure GDA00033315561300001013
in the formula (12), the first and second groups,
Figure GDA00033315561300001014
for the active power transmitted on the n-th section connecting line,
Figure GDA00033315561300001015
is the setting value of the active power of the nth section, Slink,nSet of links included in the nth cross-section, NcutThe number of the sections;
the upper and lower limits of the active and reactive output power of the wind power under the ith topological structure are constrained as follows:
Figure GDA00033315561300001016
in the formula (13), the first and second groups,
Figure GDA00033315561300001017
the lower limit of the wind power active output power at the node j is defined,
Figure GDA00033315561300001018
the upper limit of the wind power active output power at the node j is defined,
Figure GDA00033315561300001019
is the lower limit of the wind power reactive output power at the node j,
Figure GDA00033315561300001020
the upper limit of the wind power reactive output power at the node j is set;
the node voltage constraint under the ith topology is as follows:
Figure GDA00033315561300001021
in the formula (14), VminIs the lower limit of the node voltage, VmaxIs the upper limit of the node voltage;
the branch power constraint under the ith topology is as follows:
Figure GDA00033315561300001022
in the formula (15), the first and second groups,
Figure GDA0003331556130000111
the branch connecting nodes k and j transmits power,
Figure GDA0003331556130000112
for the lower limit of the transmission power of the branch connecting nodes k and j,
Figure GDA0003331556130000113
transmitting an upper limit of power for a branch connecting nodes k and j;
reconstruction time distribution unit group DwAnd (3) limiting the switching times:
0≤Dw≤Dw,max (16)
in the formula (16), Dw,maxAs a unit group DwMaximum number of switching actions;
s34, adding a wind power plant output power probability model and a node comprehensive load power demand probability model into the optimization model to form a nonlinear model between the safety margin of the power transmission network and the injection power of each node:
F＝h(X) (17)
in equation (17), h () is a nonlinear function of the injected power of each node and the grid safety margin, X is a random vector for the injected power of each node, and X ═ X1,X2,…,Xm]。
S35, obtaining an evaluation index value RSSD by solving the nonlinear model;
s36, calculating output power and comprehensive load demand X of wind power plantiOf the sampled value xi,k：
xi,k＝μi+ξi,kσi，k＝1,2,3 (18)
In the formula (18), μi、σiAre respectively variable XiMean and standard deviation ofi,kIs a sample value xi,kThe position coefficient of (a);
wherein the position coefficient xii,kThe calculation formula of (2) is as follows:
Figure GDA0003331556130000114
s37, passing position coefficient xii,kCalculating a weight coefficient omegai,k：
Figure GDA0003331556130000115
In the formula (20), λi,3And λi,4Are respectively variable XiSkewness and kurtosis ofi,1And xii,2Are respectively variable XiM is the number of nodes with injected power.
As shown in fig. 4, the wind power plant in the embodiment of the present invention is connected to a 220KV node, the load node includes a normal load and a charging load of an electric vehicle, and the loads are classified into a residential power load, an industrial power load, and a commercial power load according to load characteristics.
In the embodiment of the invention, the output power probability model of the wind power plant at each node is obtained by Monte Carlo sampling, and the wind power parameters of each node are shown in Table 1; and obtaining a node probability model of each node after the charging load of the electric automobile is added according to the conventional load characteristics.
TABLE 1
Figure GDA0003331556130000121
In the embodiment of the invention, the reactances of all branches are obtained according to the network structure and the element parameters, and then the contribution factor of each node to each branch and the standard deviation thereof are obtained; determining a transmission network security domain according to the power flow constraint of the transmission network line and the upper and lower limits of the power supply active output; and each evaluation sample corresponds to the determined output power of the wind power plant and the comprehensive load power demand, one topological state is selected from the feasible topology set of the high-voltage distribution network, so that the safety margin of the transmission network under each evaluation sample is the maximum, and the obtained RSSD is the safety margin of the transmission network of a certain evaluation sample.
As shown in fig. 5, the transmission grid security domain is formed by the upper and lower limits of the power output and the line power flow constraint, so as to ensure that all the operating points of the transmission grid operating safely are in the security domain; and expressing the safety margin of the power transmission network by using the minimum value of Euclidean distances from the operating point to each boundary of the safety domain.
As shown in fig. 6, the high-voltage distribution network is reconfigured to change the operation mode, change the position of the operation point in the safety domain, and bring the elasticity margin to the transmission network.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (2)

1. The urban power transmission network safety probability assessment method considering the elasticity margin is characterized by comprising the following steps of:
s1, initializing structures, element parameters and node injection power probability models of the power grid and the high-voltage power distribution network, wherein the node injection power probability models comprise a wind power plant output power probability model and a node comprehensive load power demand probability model;
s2, selecting estimation points of random variables in the node injection power probability model through the principle of a three-point estimation method to form a sample evaluation matrix Xr；
S3, sample matrix XrCalculating an evaluation index value of the power grid safety margin and a corresponding weight coefficient of the evaluation index value by each evaluation sample;
s4, when the evaluation index values of all the evaluation samples and the corresponding weight coefficients are obtained, the step S5 is executed, otherwise, the step S3 is executed;
s5, calculating a v-order origin moment of each evaluation sample evaluation index value through a weight coefficient, and expanding the v-order origin moment by utilizing a Cornish-fisher series to obtain the safety probability distribution of the power transmission network;
the specific steps of step S3 are:
s31, calculating the safety margin RSSD of the transmission grid branch iiThe calculation formula is as follows:
Figure FDA0003331556120000011
in the formula (4), PimaxIs the maximum transmission capacity, P, of branch iiFor the current transmission power, σ, of branch iG-iContributing factor G to branch i for each power supplym-iStandard deviation of (a)L-iContributing factor G to branch i for each node loadn-iStandard deviation of (d);
wherein each power supply contributes a factor G to branch im-iThe calculation formula of (2) is as follows:
Figure FDA0003331556120000012
in the formula (5), Δ PiIs the active output variation, Δ P, of branch iGmIs the active output variation, X, of the node m power supplyiIs the reactance of branch i, l, k are the first and last nodes of branch i, Xlm、XkmRespectively an l row and m columns and a k row and m columns in the reactance matrix;
each node load contributes factor G to branch in-iThe calculation formula of (2) is as follows:
Figure FDA0003331556120000021
in the formula (6), Δ PLnFor the variation of the load of node n, Xln、XknRespectively an n column in the l row and an n column in the k row in the reactance matrix;
s32, calculating an evaluation index value RSSD of the power grid safety margin, wherein the calculation formula is as follows:
RSSD＝min(RSSDi)i∈SL (7)
in the formula (7), SLIs a set containing all branches;
s33, maximizing an evaluation index value RSSD of the power grid safety margin through topology reconstruction of the high-voltage power distribution network, and constructing an optimization model, wherein the optimization model comprises a target function and constraint conditions;
the objective function is:
f＝max RSSD (8)
the alternating current power flow constraint under the ith topological structure is as follows:
Figure FDA0003331556120000022
in the formula (9), the reaction mixture,
Figure FDA0003331556120000023
respectively the active and reactive power of the wind farm at node j,
Figure FDA0003331556120000024
respectively the active demand and the reactive demand of the load at node j,
Figure FDA0003331556120000025
is the voltage at node k connected to node j,
Figure FDA0003331556120000026
is the voltage at the node j and,
Figure FDA0003331556120000027
to connect the conductances of the nodes k and j legs,
Figure FDA0003331556120000028
is the voltage phase difference of nodes k and j,
Figure FDA0003331556120000029
susceptance for connecting the branches k and j;
wherein the active demand of the load at node j
Figure FDA00033315561200000210
The calculation formula of (2) is as follows:
Figure FDA00033315561200000211
in the formula (10), the first and second groups,
Figure FDA00033315561200000212
to reconstruct the active load at the front node j,
Figure FDA00033315561200000213
the active load transferred at the node j under the ith topological structure after reconstruction;
reactive demand of load at node j
Figure FDA00033315561200000214
The calculation formula of (2) is as follows:
Figure FDA00033315561200000215
in the formula (11), the reaction mixture,
Figure FDA0003331556120000031
to reconstruct the anterior segmentThe reactive load at the point j is,
Figure FDA0003331556120000032
the reactive load transferred at the node j under the ith topological structure after reconstruction;
the section power constraint under the ith topology is as follows:
Figure FDA0003331556120000033
in the formula (12), the first and second groups,
Figure FDA0003331556120000034
for the active power transmitted on the n-th section connecting line,
Figure FDA0003331556120000035
is the setting value of the active power of the nth section, Slink,nSet of links included in the nth cross-section, NcutThe number of the sections;
the upper and lower limits of the active and reactive output power of the wind power under the ith topological structure are constrained as follows:
Figure FDA0003331556120000036
in the formula (13), the first and second groups,
Figure FDA0003331556120000037
the lower limit of the wind power active output power at the node j is defined,
Figure FDA0003331556120000038
the upper limit of the wind power active output power at the node j is defined,
Figure FDA0003331556120000039
is the lower limit of the wind power reactive output power at the node j,
Figure FDA00033315561200000310
the upper limit of the wind power reactive output power at the node j is set;
the node voltage constraint under the ith topological structure is as follows:
Figure FDA00033315561200000311
in the formula (14), VminIs the lower limit of the node voltage, VmaxIs the upper limit of the node voltage;
the branch power constraint under the ith topology is as follows:
Figure FDA00033315561200000312
in the formula (15), the first and second groups,
Figure FDA00033315561200000313
the branch connecting nodes k and j transmits power,
Figure FDA00033315561200000314
for the lower limit of the transmission power of the branch connecting nodes k and j,
Figure FDA00033315561200000315
transmitting an upper limit of power for a branch connecting nodes k and j;
reconstruction time distribution unit group DwAnd (3) limiting the switching times:
0≤Dw≤Dw,max (16)
in the formula (16), Dw,maxAs a unit group DwMaximum number of switching actions;
s34, adding a wind power plant output power probability model and a node comprehensive load power demand probability model into the optimization model to form a nonlinear model between the safety margin of the power transmission network and the injection power of each node:
F＝h(X) (17)
in equation (17), h () is a nonlinear function of the injected power of each node and the grid safety margin, X is a random vector for the injected power of each node, and X ═ X1,X2,…,Xm]；
S35, obtaining an evaluation index value RSSD by solving the nonlinear model;
s36, calculating output power and comprehensive load demand X of wind power plantiIs sampled byi,k：
xi,k＝μi+ξi,kσi，k＝1,2,3 (18)
In the formula (18), μi、σiAre respectively variable XiMean and standard deviation ofi,kIs a sample value xi,kThe position coefficient of (a);
wherein the position coefficient xii,kThe calculation formula of (2) is as follows:
Figure FDA0003331556120000041
s37, passing position coefficient xii,kCalculating a weight coefficient omegai,k：
Figure FDA0003331556120000042
In the formula (20), λi,3And λi,4Are respectively variable XiSkewness and kurtosis ofi,1And xii,2Are respectively variable XiM is the number of nodes with injected power.
2. The method for evaluating the safety probability of the urban power transmission network considering the elasticity margin according to claim 1, wherein the specific steps of calculating the node injection power probability model in the step S1 are as follows:
s11, calculating the output power P of the wind powerwindThe calculation formula is as follows:
Figure FDA0003331556120000043
in the formula (1), v is the wind speed, vciFor cutting into the wind speed, vrRated wind speed, vcoFor cutting out the wind speed, PrIs the rated power of the wind turbine generator,
Figure FDA0003331556120000044
s12, calculating a wind power plant output power probability model f (P)wind) The calculation formula is as follows:
Figure FDA0003331556120000051
in the formula (2), K is a Weibull distribution shape parameter, and C is a scale parameter;
s13, calculating a probability model of the comprehensive load power demand of the node at the time t, wherein the calculation formula is as follows:
Figure FDA0003331556120000052
in the formula (3), μP,t、σP,tRespectively, the active expected value and standard deviation, P, of the integrated node load at time tLFor integrated load active power demand, muCLQ,tFor normal load reactive expectation, σCLQ,tFor normal load reactive standard deviation, QLThe reactive power requirement of the comprehensive load is met.
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