CN109950901B - Active power distribution network optimized operation method based on improved information gap decision theory - Google Patents

Active power distribution network optimized operation method based on improved information gap decision theory Download PDF

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CN109950901B
CN109950901B CN201910247503.1A CN201910247503A CN109950901B CN 109950901 B CN109950901 B CN 109950901B CN 201910247503 A CN201910247503 A CN 201910247503A CN 109950901 B CN109950901 B CN 109950901B
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active power
load
power distribution
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葛晓琳
居兴
王云鹏
李振坤
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Shanghai University of Electric Power
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Abstract

The invention relates to an active power distribution network optimal operation method based on an improved information gap decision theory, which comprises the following steps of: 1) establishing an active power distribution network optimized operation model based on an improved information gap decision theory; 2) converting an optimized operation model of the active power distribution network into a mixed integer second-order cone model by introducing variables; 3) adopting a relaxation method to carry out polyhedral approximate description on the convex second-order cone and convert the mixed integer second-order cone programming model into a mixed integer linear programming model; 4) and solving according to a normalized vector constraint method to finally obtain an optimal active power distribution network scheduling operation scheme. Compared with the prior art, the method has the advantages of rapidness, reliability, high economy, comprehensive consideration of uncertainty of wind and light loads, improvement of enthusiasm of users for participating in optimized operation of the active power distribution network and the like.

Description

Active power distribution network optimized operation method based on improved information gap decision theory
Technical Field
The invention relates to the field of optimized operation of a power distribution network, in particular to an optimized operation method of an active power distribution network based on an improved information gap decision theory.
Background
With the large number of distributed power sources of different types connected to the power system, the operation and control of the distribution network becomes more complex. The operation management mode of the traditional power distribution network is gradually changed from passive to active, and the concept of the active power distribution network is proposed. The research on the influence of uncertainty of distributed power supply output and load demand on the optimized operation of the active power distribution network has attracted extensive attention. However, the influence of uncertainty of output and load demand of various distributed power supplies on the optimized operation of the active power distribution network is considered by the fresh scholars at the same time. Moreover, the research results of the above documents have the following disadvantages: on one hand, the problem caused by uncertainty cannot be completely resisted due to excessive dependence on historical data, and on the other hand, the established model is mostly nonlinear, the solving speed is low, and the accuracy of the solving result is difficult to ensure.
Haim proposes the information gap decision theory. The method does not depend on historical data, is simple in modeling, and is suitable for an active power distribution network optimization operation model with large uncertainty of wind and light loads. The conventional information gap decision theory method considers that the fluctuation intervals of the uncertain factors are equidistant, so that the solving result of the fluctuation intervals of the uncertain factors is too large or too small.
In addition, the traditional active power distribution network optimization operation model is based on a linear equation set of direct current flow, the calculation speed is high, and the occupied memory is small. However, the direct current power flow model is obtained by simplification on the basis of the alternating current power flow model, and the assumption is that the direct current power flow model can be well satisfied in an extra-high voltage system. Therefore, the calculation result based on the model of the dc power flow has a certain error.
Therefore, an active power distribution network optimal operation method based on an improved information gap decision theory is urgently needed, the influence of the uncertainty of wind and light load on the optimal operation of the active power distribution network can be comprehensively considered, and the established model can be rapidly and accurately solved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an active power distribution network optimization operation method based on an improved information gap decision theory.
The purpose of the invention can be realized by the following technical scheme:
an active power distribution network optimized operation method based on an improved information gap decision theory comprises the following steps:
1) establishing an active power distribution network optimized operation model based on an improved information gap decision theory;
2) converting an optimized operation model of the active power distribution network into a mixed integer second-order cone model by introducing variables;
3) adopting a relaxation method to carry out polyhedral approximate description on the convex second-order cone and convert the mixed integer second-order cone programming model into a mixed integer linear programming model;
4) and solving according to a normalized vector constraint method to finally obtain an optimal active power distribution network scheduling operation scheme.
In the step 1), the objective function of the active power distribution network optimization operation model is as follows:
max(Zwa,-Zwb,Zva,-Zvb,-Zla,Zlb)
wherein Z iswaAnd ZwbMaximum and minimum uncertainty, Z, of the wind power output, respectivelyvaAnd ZvbRespectively, maximum and minimum uncertainty of photovoltaic output, ZlaAnd ZlbThe maximum and minimum uncertainty of the load prediction deviation, respectively.
In the step 1), the constraint conditions of the active power distribution network optimization operation model include:
wind power information gap constraint:
Figure GDA0002591729660000021
wherein the content of the first and second substances,
Figure GDA0002591729660000022
to be the active power output of the w-th fan at the time t under the scene c,
Figure GDA0002591729660000023
predicting a wind power output value of the w-th fan at the time t;
photovoltaic information gap constraint:
Figure GDA0002591729660000024
wherein the content of the first and second substances,
Figure GDA0002591729660000025
the active power output of the v-th photovoltaic power station at the moment t under the scene c,
Figure GDA0002591729660000026
predicting a force value for the photovoltaic of the v-th photovoltaic at the time t;
and (3) load information gap constraint:
Figure GDA0002591729660000027
wherein the content of the first and second substances,
Figure GDA0002591729660000028
the active demand of the ith load at time t in scenario c,
Figure GDA0002591729660000029
load prediction value of the first load at the time t;
a target cost constraint.
Figure GDA0002591729660000031
Wherein, C is the operation cost of the active power distribution network, C is the scene number, when C is 1, the worst operation scene is corresponding, when C is 2, the most ideal operation scene is corresponding,chfor the corresponding bias factor in the worst scenario,cothe value range of the deviation factor corresponding to the optimal scene is [0,1 ], CoObtaining an optimal solution for the original deterministic model;
and (4) power balance constraint.
Figure GDA0002591729660000032
Figure GDA0002591729660000033
Figure GDA0002591729660000034
Figure GDA0002591729660000035
Figure GDA0002591729660000036
Wherein omegaiIs the node set connected to node i, n is the total number of nodes,
Figure GDA00025917296600000310
the active power injected by the node i at the moment t in the scenario c,
Figure GDA00025917296600000311
reactive power injected at time t for node i under scene c, GijAnd BijConductance and susceptance, θ, between node i and node j, respectivelyij,cThe line impedance angle between node i and node j in scenario c,
Figure GDA0002591729660000037
respectively a correlation matrix between a gas turbine, a fan, a photovoltaic power station, a demand load, an interruptible load and a node i,
Figure GDA0002591729660000038
respectively the active power output of the w-th fan at the moment t, the active power output of the v-th photovoltaic power station at the moment t, the active demand of the l-th load at the moment t and the active load reduction capacity of the k-th load at the moment t under the scene c,
Figure GDA0002591729660000039
respectively representing the reactive power output of the d-th gas turbine at the moment t, the reactive power output of the w-th fan at the moment t, the reactive power output of the v-th photovoltaic power station at the moment t, the reactive power demand of the l-th load at the moment t and the reactive power reduction capacity of the k-th load at the moment t under the scene c;
node voltage constraint:
Vi,c,min≤Vi,c≤Vi,c,max
line power constraint:
Sij,c≤Sij,c,max
wherein, Vi,cIs the voltage of node i under scenario c, Vi,c,minAnd Vi,c,maxRespectively, the minimum and maximum amplitudes, V, of the node voltage under the scene ci,cAnd Sij,cRespectively representing the node voltage under the scene c and the power flow amplitude on the line;
and (3) output constraint of the distributed power supply:
Figure GDA0002591729660000041
Figure GDA0002591729660000042
Figure GDA0002591729660000043
Figure GDA0002591729660000044
Figure GDA0002591729660000045
Figure GDA0002591729660000046
Figure GDA0002591729660000047
Figure GDA0002591729660000048
Figure GDA0002591729660000049
wherein the content of the first and second substances,
Figure GDA00025917296600000410
and
Figure GDA00025917296600000411
respectively the minimum and maximum active output values of the d-th gas turbine at the time t;
Figure GDA00025917296600000412
and
Figure GDA00025917296600000413
respectively the minimum and maximum active output values of the w-th fan at the time t,
Figure GDA00025917296600000414
and
Figure GDA00025917296600000415
respectively the minimum and maximum active output values of the photovoltaic power station at the moment t,
Figure GDA00025917296600000416
and
Figure GDA00025917296600000417
respectively the minimum and maximum reactive power takeoff values of the d-th gas turbine at time t,
Figure GDA00025917296600000418
and
Figure GDA00025917296600000419
respectively the minimum and maximum reactive power output values of the w-th fan at the time t,
Figure GDA00025917296600000420
and
Figure GDA00025917296600000421
respectively the minimum and maximum reactive power output values of the photovoltaic power station at the moment t,
Figure GDA00025917296600000422
the capacities of the d-th gas turbine, the w-th fan and the v-th photovoltaic cell in the scene c are respectively set;
interruptible load constraint:
Figure GDA00025917296600000423
wherein the content of the first and second substances,
Figure GDA00025917296600000424
and
Figure GDA00025917296600000425
respectively the minimum and maximum active values of the k-th load allowed to be interrupted at the time t;
and g, the constraint condition that the feeder line sells and purchases electricity to and from the power grid at the time t.
Figure GDA0002591729660000051
Figure GDA0002591729660000052
d3+d4＝1
Wherein d is3And d4Is a binary variable, and is characterized in that,
Figure GDA0002591729660000053
and
Figure GDA0002591729660000054
and the maximum values of electricity sold to the power grid and electricity purchased from the power grid at the moment t by the g feeder line are respectively.
The step 2) specifically comprises the following steps:
21) introducing intermediate variables to convert a nonlinear active power distribution network optimization operation model into a second-order cone planning problem, wherein the intermediate variables comprise:
Figure GDA0002591729660000055
Figure GDA0002591729660000056
Mij,c＝Vi,cVj,csinθij,c
Zij,c＝Vi,cVj,ccosθij,c
wherein the content of the first and second substances,
Figure GDA0002591729660000057
the active power output of the d-th gas turbine at the moment t;
22) and carrying out cone conversion on the operation cost of the distributed power supply, a system power flow constraint function, a system node voltage and line power constraint function and distributed power supply output constraint respectively to obtain a mixed integer second-order cone model.
The method specifically comprises the following steps:
22) the cone transition in the cost of operating a distributed power supply,
Figure GDA0002591729660000058
for a non-linear function, it is converted to a linear function as follows:
Figure GDA0002591729660000059
Figure GDA00025917296600000510
obtaining polyhedral approximate description of a second-order cone after relaxing variables, and obtaining a formula
Figure GDA00025917296600000511
The relaxation translates into the following cone constraint:
Figure GDA00025917296600000512
Figure GDA00025917296600000513
23) and (3) cone conversion of the system power flow constraint function, namely converting the system power flow constraint function into a linear function as follows:
Figure GDA00025917296600000514
Figure GDA00025917296600000515
24) and (3) cone conversion of a system node voltage and line power constraint function, wherein the system node voltage and line power constraint function is converted into the following cone function:
Figure GDA0002591729660000061
Figure GDA0002591729660000062
Figure GDA0002591729660000063
the above formula relaxation is converted into the following cone constraint:
Figure GDA0002591729660000064
at this time, the feasible region has already relaxed into a second-order cone, and a convex feasible region is formed and is converted into the following second-order cone form through transformation:
Figure GDA0002591729660000065
two three-dimensional second-order cone joint representations can be used:
Figure GDA0002591729660000066
Figure GDA0002591729660000067
25) cone conversion of distributed power supply output constraint:
Figure GDA0002591729660000068
Figure GDA0002591729660000069
Figure GDA00025917296600000610
at this time, the whole model is converted into MI-SOCP, and the solution is difficult, so that the MI-SOCP problem is converted into the MILP problem solution.
In the step 3), the polyhedral approximation expression of the convex second-order cone is as follows:
Figure GDA00025917296600000611
α0≥|X1|
β0≥|X2|
Figure GDA00025917296600000612
Figure GDA00025917296600000613
αk≤X3
Figure GDA0002591729660000071
wherein k is generally 11, X1，X2，X3Is a set of optimized variables which represent different meanings for different cone-to-cone constraint formulas and cone-to-cone constraint X for the operation cost of the distributed power supply1，X2，X3Respectively represent
Figure GDA0002591729660000072
Figure GDA0002591729660000073
Cone conversion for the system node voltage and line power constraint functions yields two cone constraints, the first cone constraint
Figure GDA0002591729660000074
In (C) X1，X2，X3Each represents Mij,c，Zij,c，Qij,cSecond cone constraint
Figure GDA0002591729660000075
In (C) X1，X2，X3Each represents Qij,c，
Figure GDA0002591729660000076
Figure GDA0002591729660000077
Three cone constraints are generated by cone conversion of distributed power supply output constraint, wherein the first cone constraint
Figure GDA0002591729660000078
In (C) X1，X2，X3Respectively represent
Figure GDA0002591729660000079
Second cone constraint
Figure GDA00025917296600000710
In (C) X1，X2，X3Respectively represent
Figure GDA00025917296600000711
Third cone constraint
Figure GDA00025917296600000712
In (C) X1，X2，X3Respectively represent
Figure GDA00025917296600000713
Is a sufficiently small relaxation variable, defined as
Figure GDA00025917296600000714
When k is 11, 6 × 10-7，α0And beta0Is an arbitrary non-negative number, αmAnd betamIs an arbitrary non-negative number, αkAnd betakI.e. represents alpha11And beta11。
In the step 4), the normalized vector constraint method specifically includes the following steps:
41) and calculating the anchor point. For simplicity of description, it is assumed that only 3 initial objective function variables are uncertainty of wind power, photovoltaic power and load, and are recorded as Zw、Zv、ZlRespectively find Zw、Zv、ZlRespectively obtaining the anchor points
Figure GDA00025917296600000715
42) Normalization of feasible fields, defining the point of utopia:
Zz＝[Zw*(Xw*),Zv*(Xv*),Zl*(Xl*)]
definition of dw、dvAnd dlAre respectively as
Figure GDA00025917296600000716
And
Figure GDA00025917296600000717
to point Z of UtoxpointzThe distance of (c).
Any point in the feasible region can be normalized to
Figure GDA00025917296600000718
Figure GDA00025917296600000719
43) Defining the Uutopia vector
Figure GDA00025917296600000720
Are respectively provided with directions of
Figure GDA00025917296600000721
Point of direction
Figure GDA00025917296600000722
Point of direction
Figure GDA00025917296600000723
Point of direction
Figure GDA00025917296600000724
Figure GDA00025917296600000725
Figure GDA00025917296600000726
Figure GDA0002591729660000081
44) Calculating the normalized average increment of the bisector points:
Figure GDA0002591729660000082
in the formula: m is the length ratio of each segment; m is1Is the total number of stages.
Step5 generates Uutopia segmentation points:
Figure GDA0002591729660000083
in the formula:
Figure GDA0002591729660000084
is a segmentation point vector;
Figure GDA0002591729660000088
k 11,2,3 is incremented in steps of M and satisfies the following constraint:
Figure GDA0002591729660000085
Figure GDA0002591729660000086
step6 generates a pareto point. The pareto points are obtained by adopting a point set uniformly distributed on the Utoban and solving the following model:
the solution of the original objective function is similar to the above steps, and will not be described herein again.
By the formula alpha0≥|X1The absolute value sign of | is defined as M is a large enough positive number, and an auxiliary variable a is introduced1、a2、d1、d2And when a is1When > 0, there is d 11, otherwise d 10; when a is2When > 0, there is d 21, otherwise d2＝0。
Let X1＝-a1+a2
and-Md1≤X1≤Md2
0≤a1≤Md1
0≤a2≤Md2
d1+d2＝1
Then | X1|＝a1+a2
Similarly, formula β can be removed0≥|X2|、
Figure GDA0002591729660000087
The absolute value sign of k is 1,2,3.
Compared with the prior art, the invention has the following advantages:
firstly, the method is quick and reliable: the method disclosed by the invention can quickly and reliably obtain the uncertainty of the wind-solar load.
Secondly, the economy is high: the method disclosed by the invention can obtain smaller operation cost, and can ensure that the operation cost of the active power distribution network is lower than an expected value when the wind and light load fluctuates in a certain interval.
Thirdly, comprehensively considering uncertainty of wind and light loads: the uncertainty of the wind and light load has obvious influence on the optimized operation result of the active power distribution network, and the influence of the uncertainty of the wind and light load on the optimized operation of the active power distribution network is not comprehensively considered, so that deviation is generated on the estimation of the volatility of the scheduling target, and therefore, a scheduling method comprehensively considering the uncertainty of the wind and light load is considered, and a scheduling scheme with higher feasibility can be obtained.
Fourthly, improving the enthusiasm of the user in participating in the optimization operation of the active power distribution network: the method can effectively prompt the user to actively participate in the operation management of the active power distribution network, and therefore, the method has great potential for solving the problem that the wind-solar-load uncertainty influences the optimized operation of the active power distribution network.
Drawings
FIG. 1 is a network architecture diagram of an IEEE33 node power distribution system
FIG. 2 is a graph illustrating the difference between the wind-solar load uncertainty of the proposed method and the conventional method.
Fig. 3 is a comparison graph of the operating cost of the active power distribution network obtained by the method of the present invention and the conventional method.
Fig. 4 is a graph of the operating cost of the active power distribution network in different intervals and under different scenes.
Fig. 5 is a graph showing a relationship between the equivalent load and the load shedding load.
FIG. 6 is a flow chart of a method of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
As shown in FIG. 6, the invention provides an active power distribution network optimization operation method based on an improved information gap decision theory, firstly, an active power distribution network optimization operation mathematical model based on the improved information gap decision theory is established, the model takes the uncertainty of wind, light and load as the maximum target, and simultaneously satisfies the constraint condition of the active power distribution network safety operation, and the established model is a nonlinear model.
Secondly, the established model is converted into a standard second-order cone model through the introduction of variables to be solved.
The convex second-order cone is subjected to polyhedral approximation description by adopting a 'relaxation' method proposed by Ben-Tal and Nemirovski, and the MI-SOCP solution is difficult, so that the MI-SOCP is converted into MILP by utilizing a mathematical method.
The concrete solving steps are as follows:
step 1: establishing an active power distribution network optimization operation model based on an improved information gap decision theory;
step 2: converting the established nonlinear model into a standard second-order cone model by introducing variables;
and step 3: converting the established MI-SOCP model into an MILP model by a mathematical method;
and 4, step 4: inputting data, including electricity price, wind power, photovoltaic output data and coincidence prediction data;
and 5: solving the optimal operation cost of the active power distribution network optimized operation model without considering the wind-solar-load uncertainty;
step 6: setting the obtained optimal cost as a reference value of an improved information gap decision theoretical model;
and 7: converting the multi-target problem into a single-target problem by using a normalized vector constraint method to solve;
and 8: selecting a scene, and judging whether the scene is the worst scene;
and step 9: if the scene is the worst scene, setting a deviation factor under the worst scene;
step 10: if the scene is the optimal scene, setting a deviation factor under the optimal scene;
step 11: and solving the improved model to obtain the maximum and minimum running cost and the uncertainty of the air pipe load.
The method comprises the steps of firstly modeling the uncertainty of wind, light and load, establishing an active power distribution network optimization operation model based on an improved information gap decision theory, then converting an established nonlinear model into a standard second-order cone model by introducing variables, then relaxing the established model by a relaxation method, converting an MI-SOCP model into an MILP model by removing absolute values, converting a multi-target problem into a single-target problem by using a normalized vector constraint method, and finally performing example simulation on an improved IEEE33 node.
The results of solving the MI-SOCP and MILP models are shown in Table 1, and it can be seen from Table 1 that the results of solving the two models are relatively close, but the solving time of the MILP model is much shorter than that of the MISOCP model. Therefore, the MILP obtained after the 'relaxation' is adopted has more feasibility and adaptability; the uncertainty values of the wind-solar load under different deviation factors are shown in table 2, and it can be known from the analysis in table 2 that the uncertainty of the wind-solar load increases with the increase of the deviation factors. In an ideal scene, when the deviation factor is increased, the wind power and photovoltaic output can be increased, the load value can be reduced, and the running cost of the active power distribution network can be reduced; on the contrary, in the worst scene, when the deviation factor is increased, the wind power and photovoltaic output can be reduced, the generated power shortage can be shared by the conventional units, and the load value can be increased. The cost of ADN operation must be increased.
TABLE 1 comparison of MI-SOCP and MILP model solution results
Method of producing a composite material Zwa/％ Zwb/％ Zva/％ Zvb/％ Zla/％ Zlb/s Time/s
MILP 14.70 0 8.25 0 1.89 1.81 ＜360
MISOCP 14.68 0 8.24 0 1.87 1.80 ＞900
TABLE 2 uncertainty values of wind and light loads found under different deviation factors
Figure GDA0002591729660000101
Figure GDA0002591729660000111
The structure of the improved IEEE33 node power distribution system network is shown in figure 1; the difference between the wind-solar load uncertainty obtained by the method provided by the invention and the traditional method is shown in figure 2, and as can be seen from figure 2, the difference between the uncertainty obtained by the improved model and the traditional model does not exceed 0.08% at most. Therefore, the improved model established by the invention has more accurate solving result.
The operation cost of the active power distribution network obtained by the method of the invention and the traditional method is shown in figure 3, and as can be seen from figure 3, the economic benefit obtained by the improved model established by the invention is better.
The operation cost of the active power distribution network in different intervals and different scenes is shown in fig. 4, and as can be seen from fig. 4, the method and the device can ensure that the operation cost of the active power distribution network in different scenes can be lower than the expected cost, and the economy is higher.
The relationship between the equivalent load and the load shedding load is shown in fig. 5, and as can be seen from fig. 5, the method and the device can mobilize the user to actively participate in the operation management of the active power distribution network, and can play a role in peak clipping. Therefore, the method provided by the invention has the advantages of high calculation precision and high calculation speed in solving the optimization operation problem of the active power distribution network. In addition, the influence of the uncertainty of the wind-solar load on the optimized operation of the active power distribution network is comprehensively considered, so that the scheduling method is more consistent with the actual operation condition.

Claims (3)

1. An active power distribution network optimized operation method based on an improved information gap decision theory is characterized by comprising the following steps:
1) an active power distribution network optimization operation model based on an improved information gap decision theory is established, and the objective function of the active power distribution network optimization operation model is as follows:
max(Zwa,-Zwb,Zva,-Zvb,-Zla,Zlb)
wherein Z iswaAnd ZwbMaximum and minimum uncertainty, Z, of the wind power output, respectivelyvaAnd ZvbRespectively, maximum and minimum uncertainty of photovoltaic output, ZlaAnd ZlbRespectively for load predictionMaximum minimum uncertainty of deviation;
the constraint conditions include:
wind power information gap constraint:
Figure FDA0002629862230000011
wherein the content of the first and second substances,
Figure FDA0002629862230000012
to be the active power output of the w-th fan at the time t under the scene c,
Figure FDA0002629862230000013
predicting a wind power output value of the w-th fan at the time t;
photovoltaic information gap constraint:
Figure FDA0002629862230000014
wherein the content of the first and second substances,
Figure FDA0002629862230000015
the active power output of the v-th photovoltaic power station at the moment t under the scene c,
Figure FDA0002629862230000016
predicting a force value for the photovoltaic of the v-th photovoltaic at the time t;
and (3) load information gap constraint:
Figure FDA0002629862230000017
wherein the content of the first and second substances,
Figure FDA0002629862230000018
the active demand of the ith load at time t in scenario c,
Figure FDA0002629862230000019
load prediction value of the first load at the time t;
target cost constraints:
Figure FDA00026298622300000110
wherein, C is the operation cost of the active power distribution network, C is the scene number, when C is 1, the worst operation scene is corresponding, when C is 2, the most ideal operation scene is corresponding,chfor the corresponding bias factor in the worst scenario,cothe value range of the deviation factor corresponding to the optimal scene is [0,1 ], CoObtaining an optimal solution for the original deterministic model;
and power balance constraint:
Figure FDA0002629862230000021
Figure FDA0002629862230000022
Figure FDA0002629862230000023
Figure FDA0002629862230000024
Figure FDA0002629862230000025
wherein omegaiIs the node set connected to node i, n is the total number of nodes,
Figure FDA0002629862230000026
the active power injected by the node i at the moment t in the scenario c,
Figure FDA0002629862230000027
reactive power injected at time t for node i under scene c, GijAnd BijConductance and susceptance, θ, between node i and node j, respectivelyij,cThe line impedance angle between node i and node j in scenario c,
Figure FDA0002629862230000028
respectively a correlation matrix between a gas turbine, a fan, a photovoltaic power station, a demand load, an interruptible load and a node i,
Figure FDA0002629862230000029
respectively the active power output of the w-th fan at the moment t, the active power output of the v-th photovoltaic power station at the moment t, the active demand of the l-th load at the moment t and the active load reduction capacity of the k-th load at the moment t under the scene c,
Figure FDA00026298622300000210
respectively representing the reactive power output of the d-th gas turbine at the moment t, the reactive power output of the w-th fan at the moment t, the reactive power output of the v-th photovoltaic power station at the moment t, the reactive power demand of the l-th load at the moment t and the reactive power reduction capacity of the k-th load at the moment t under the scene c;
node voltage constraint:
Vi,c,min≤Vi,c≤Vi,c,max
line power constraint:
Sij,c≤Sij,c,max
wherein, Vi,cIs the voltage of node i under scenario c, Vi,c,minAnd Vi,c,maxRespectively, the minimum and maximum amplitudes, V, of the node voltage under the scene ci,cAnd Sij,cRespectively representing the node voltage under the scene c and the power flow amplitude on the line;
and (3) output constraint of the distributed power supply:
Figure FDA0002629862230000031
Figure FDA0002629862230000032
Figure FDA0002629862230000033
Figure FDA0002629862230000034
Figure FDA0002629862230000035
Figure FDA0002629862230000036
Figure FDA0002629862230000037
Figure FDA0002629862230000038
Figure FDA0002629862230000039
wherein the content of the first and second substances,
Figure FDA00026298622300000310
and
Figure FDA00026298622300000311
respectively the minimum and maximum active output values of the d-th gas turbine at the time t;
Figure FDA00026298622300000312
and
Figure FDA00026298622300000313
respectively the minimum and maximum active output values of the w-th fan at the time t,
Figure FDA00026298622300000314
and
Figure FDA00026298622300000315
respectively the minimum and maximum active output values of the photovoltaic power station at the moment t,
Figure FDA00026298622300000316
and
Figure FDA00026298622300000317
respectively the minimum and maximum reactive power takeoff values of the d-th gas turbine at time t,
Figure FDA00026298622300000318
and
Figure FDA00026298622300000319
respectively the minimum and maximum reactive power output values of the w-th fan at the time t,
Figure FDA00026298622300000320
and
Figure FDA00026298622300000321
respectively the minimum and maximum reactive power output values of the photovoltaic power station at the moment t,
Figure FDA00026298622300000322
the capacities of the d-th gas turbine, the w-th fan and the v-th photovoltaic cell in the scene c are respectively set;
interruptible load constraint:
Figure FDA00026298622300000323
wherein the content of the first and second substances,
Figure FDA00026298622300000324
and
Figure FDA00026298622300000325
respectively the minimum and maximum active values of the k-th load allowed to be interrupted at the time t;
the constraint conditions that the g feeder sells and purchases electricity to and from the power grid at the time t;
Figure FDA00026298622300000326
Figure FDA00026298622300000327
d3+d4＝1
wherein d is3And d4Is a binary variable, and is characterized in that,
Figure FDA00026298622300000328
and
Figure FDA00026298622300000329
the maximum values of electricity sold to the power grid and electricity purchased from the power grid by the g feeder line at the time t are respectively;
2) converting an optimized operation model of the active power distribution network into a mixed integer second-order cone model by introducing variables;
3) adopting a relaxation method to carry out polyhedral approximate description on the convex second-order cone and convert the mixed integer second-order cone programming model into a mixed integer linear programming model;
4) and solving according to a normalized vector constraint method to finally obtain an optimal active power distribution network scheduling operation scheme.
2. The active power distribution network optimal operation method based on the improved information gap decision theory as claimed in claim 1, wherein the step 2) specifically comprises the following steps:
21) introducing intermediate variables to convert a nonlinear active power distribution network optimization operation model into a second-order cone planning problem, wherein the intermediate variables comprise:
Figure FDA0002629862230000041
Figure FDA0002629862230000042
Mij,c＝Vi,cVj,csinθij,c
Zij,c＝Vi,cVj,ccosθij,c
wherein the content of the first and second substances,
Figure FDA0002629862230000043
the active power output of the d-th gas turbine at the moment t;
22) and carrying out cone conversion on the operation cost of the distributed power supply, a system power flow constraint function, a system node voltage and line power constraint function and distributed power supply output constraint respectively to obtain a mixed integer second-order cone model.
3. The active power distribution network optimal operation method based on the improved information gap decision theory as claimed in claim 1, wherein in the step 3), the polyhedral approximation expression of the convex second order cone is:
Figure FDA0002629862230000044
α0≥|X1|
β0≥|X2|
Figure FDA0002629862230000045
Figure FDA0002629862230000046
αk≤X3
Figure FDA0002629862230000047
wherein, X1、X2、X3Is a set of optimization variables, is a relaxation variable, alpha0、β0、αi、βiAre all non-negative constants, and k takes the value of 11.
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