CN113076626B - Distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization - Google Patents

Distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization Download PDF

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CN113076626B
CN113076626B CN202110283493.4A CN202110283493A CN113076626B CN 113076626 B CN113076626 B CN 113076626B CN 202110283493 A CN202110283493 A CN 202110283493A CN 113076626 B CN113076626 B CN 113076626B
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廖小兵
张敏
李自成
王后能
曾丽
熊涛
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Abstract

The invention provides a distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization. Firstly, maximizing distributed photovoltaic grid-connected capacity in a power distribution network as a target function, and considering constraint conditions such as distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint, node voltage constraint and the like; and then establishing a fuzzy set of moment uncertainty of distributed photovoltaic output and load demand, considering node voltage and branch transmission capacity out-of-limit opportunity constraints, reconstructing a distributed photovoltaic limit grid-connected capacity optimization model under moment uncertainty input by adopting cone linear dual transformation and S-lemma, and performing piecewise linearization to solve the model into a mixed integer linear programming model, so that a commercial solver Cplex can be directly called for solving the problem.

Description

Distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization
Technical Field
The invention belongs to the technical field of distributed power generation grid connection, and particularly relates to a distributed photovoltaic limit grid connection capacity evaluation method based on distributed robust optimization.
Background
The distributed photovoltaic power generation has the advantages of high flexibility, low investment, short construction period, small occupied area and the like, and meets the strategic requirements of national sustainable development. With the increasing maturity of distributed photovoltaic power generation technology and a multi-level market reward mechanism, planning and construction of a distributed photovoltaic power generation project are rapidly promoted, and a large number of distributed photovoltaic power stations are directly merged into a power distribution network. Distributed photovoltaic power generation is different from a traditional power supply, the output of the distributed photovoltaic power generation has randomness and fluctuation, the stability is poor, the distributed photovoltaic power generation is easily influenced by various factors such as seasons, weather and the like, and the distributed photovoltaic power generation cannot be completely accepted as a stable power supply. Therefore, the acceptance capability of the distribution network to the distributed photovoltaic, namely the limit grid-connected capacity of the distributed photovoltaic, needs to be accurately evaluated and analyzed, and the method plays an important role in promoting the safe and economic consumption of the distributed photovoltaic.
At present, the research on the distributed photovoltaic limit grid-connected capacity evaluation method at home and abroad is mainly divided into a simulation method based on multiple simulation verification and an optimization method based on mathematical programming. The simulation method based on multiple times of simulation verification simulates the running state of the power distribution network after the distributed photovoltaic access through simulation software and verifies the safety constraints one by one, so the method is simple to implement and consumes a large amount of time. The optimization method based on mathematical programming aims at maximizing the limit grid-connected capacity of the distributed photovoltaic, takes various safety constraints, load flow equation constraints and the like of the power distribution network as constraint conditions, and adopts different mathematical programming methods to solve. The method has the advantages that the established distributed photovoltaic limit grid-connected capacity optimization model is accurate and the optimization result is reliable, but different results are generated under different constraint conditions, so that the optimization model needs to be accurately established.
The traditional deterministic distributed photovoltaic limit grid-connected capacity optimization model does not consider the fluctuation of distributed photovoltaic output, and is difficult to be applied to distributed photovoltaic limit grid-connected capacity evaluation. For this purpose, a stochastic programming model, a robust programming model, and an opportunity constrained programming model are introduced into the distributed photovoltaic grid-connected capacity evaluation. The robust scale of the distributed photovoltaic limit grid-connected capacity does not need to establish an accurate probability model, only an interval set of photovoltaic output needs to be obtained, but the robust planning result is conservative, and the distributed photovoltaic is not favorably maximally absorbed. The opportunity constraint planning model means that the distributed photovoltaic limit grid-connected capacity is allowed not to meet certain inequality constraint conditions of the power distribution network, but the probability of meeting the constraint conditions of the power distribution network is not lower than a preset confidence level. Although the opportunity constrained planning model of the distributed photovoltaic grid-connected capacity is relatively close to reality, accurate probability description or empirical assumption on the distributed photovoltaic output or the prediction error is still required.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the distributed photovoltaic limit grid-connected capacity evaluation method based on distribution robust optimization is provided and used for accurately obtaining probability distribution parameters in distributed photovoltaic limit grid-connected capacity evaluation.
The technical scheme adopted by the invention for solving the technical problems is as follows: the distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization comprises the following steps:
s1: initializing, inputting power distribution network line parameters, distributed photovoltaic output and load prediction reference values;
s2: establishing a distribution network limit distributed photovoltaic grid-connected capacity optimization model; taking the maximum distributed photovoltaic grid-connected capacity in the power distribution network as a target function, and introducing constraint conditions including distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint and node voltage constraint;
s3: establishing a moment uncertainty fuzzy set of distributed photovoltaic output and load requirements;
s4: reconstructing node voltage and branch transmission capacity out-of-limit opportunity constraint conditions;
s5: linearizing the constraint condition reconstructed in the step S4;
s6: and (5) solving the mixed integer linear programming model established and converted in the steps S1 to S5 through a commercial solver, and outputting the distributed photovoltaic limit grid-connected capacity.
According to the scheme, the step S2 specifically comprises the following steps:
s21: setting distributed photovoltaic grid-connected capacity at node i as S i With a distributed set of photovoltaic access nodes as Ψ PV Maximizing the distributed photovoltaic grid-connected capacity in the power distribution network as a target function:
Figure BDA0002979445520000021
s22: the constraint conditions introduced for optimizing the distributed photovoltaic grid-connected capacity in the power distribution network comprise: distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint and node voltage constraint.
Further, in the step S22, the actual output active power of the distributed photovoltaic system at the time t of the node i is set to
Figure BDA0002979445520000022
Reactive power of
Figure BDA0002979445520000023
The distributed photovoltaic power conversion coefficient of the node i in the t period is
Figure BDA0002979445520000024
The power factor of the distributed photovoltaic of the node i in the period t is
Figure BDA0002979445520000025
And if the evaluation period of the distributed photovoltaic grid-connected capacity is T, the distributed photovoltaic operation constraint is as follows:
Figure BDA0002979445520000031
further, in the step S22, the actual active power demand of the load of the node i at the time t is set as
Figure BDA0002979445520000032
The reactive power requirement is
Figure BDA0002979445520000033
The active power of the branch ij flowing from the node i to the node j at the moment t is P ij,t And the reactive power is Q ij,t (ii) a The set of all nodes of the power distribution network is psi n Then the node power balance constraint is:
Figure BDA0002979445520000034
further, in step S22, the maximum transmission capacity of the branch ij is set as S ij,max Then the branch transmission capacity constraint is:
Figure BDA0002979445520000035
at this moment, the branch transmission capacity constraint is a cone constraint, and the polyhedron norm is adopted to be approximately:
Figure BDA0002979445520000036
further, in step S22, the voltage amplitude of the node i at time t is set as V i,t The square of the voltage amplitude is U i,t All branches in the distribution network are grouped into psi b The resistance of branch ij is r ij Reactance value of x ij Then, the flow constraint is described as follows by using a Distflow branch flow model:
Figure BDA0002979445520000037
defining the square L of the magnitude of the current of the branch with the new variable ij,t Comprises the following steps:
Figure BDA0002979445520000038
let the introduced virtual intermediate variable be u ij,t Then, after the above formula is relaxed, the above formula is jointly expressed by two three-dimensional second-order cones:
Figure BDA0002979445520000041
Figure BDA0002979445520000042
let K =1,2, \ 8230, K, K is the number of facets, generally 11 is taken to satisfy the approximate precision of the second order cone; let a k 、b k 、m k 、n k And further adopting polyhedron approximation as the virtual variables introduced for polyhedron linearization:
Figure BDA0002979445520000043
Figure BDA0002979445520000044
the power flow constraint equation is:
Figure BDA0002979445520000051
Figure BDA0002979445520000052
Figure BDA0002979445520000053
further, in the step S22, the upper bound of the square of the node voltage amplitude is set as U i,max The lower boundary is U i,min ，U i,t ＝U ref ,
Figure BDA0002979445520000054
The node voltage constraint is then:
Figure BDA0002979445520000055
further, in the step S3, the specific steps are as follows:
introducing random variables
Figure BDA0002979445520000056
Defining distributed photovoltaic actual power conversion coefficients
Figure BDA0002979445520000057
And load active power and load reactive power
Figure BDA0002979445520000058
Comprises the following steps:
Figure BDA0002979445520000059
let xi be the probability density function f (xi), and the support set of the probability density function f (xi) be S ∈ R 2 (ii) a Random variable
Figure BDA00029794455200000510
Has a first moment confidence interval of
Figure BDA00029794455200000511
Random variable
Figure BDA00029794455200000512
Has a first moment confidence interval of
Figure BDA00029794455200000513
Random variable
Figure BDA00029794455200000514
The second order moment confidence interval of
Figure BDA00029794455200000515
Random variable
Figure BDA00029794455200000516
Is a second order moment confidence interval of
Figure BDA00029794455200000517
Then it is difficult to obtain the randomUnder the condition of accurate probability distribution information of the variable xi, counting first moment information and second moment information of the random variable xi through limited historical data, and defining a xi fuzzy set based on moment uncertainty as follows:
Figure BDA0002979445520000061
further, in the step S4, the specific steps are: setting an opportunity constraint confidence parameter as epsilon, and indicating that the probability of node voltage and branch transmission capacity out-of-limit is lower than epsilon; the out-of-limit opportunity constraints on node voltage and branch transmission capacity are:
Pr{U i,min ≤U i,t ≤U i,max }≥1-ε，
Figure BDA0002979445520000062
let affine coefficient be A = [ A = 1 ,A 2 ]The opportunity constraint conditions are collectively expressed as:
Pr{A T ξ≤B}≥1-ε；
converting the chance constraint into a moment uncertainty fuzzy set based on the moment uncertainty fuzzy set established in the step S3
Figure BDA0002979445520000063
The left side of the above formula gives Pr { A T ξ ≦ B } the worst case probability bound on the fuzzy set D, equivalent to the target value of the following optimization problem:
Figure BDA0002979445520000064
Figure BDA0002979445520000065
Figure BDA0002979445520000066
Figure BDA0002979445520000067
in which an indication function pi is arranged c (xi) use in judgment A T B is less than or equal to xi; if A T Xi is less than or equal to B, then pi c (xi) is 1, if A T B is less than or equal to xi, pi c (xi) is 0; q is arranged,
Figure BDA0002979445520000068
α n 、β n And upsilon ≧ 0 is a dual variable, and the dual transformation of cone linearity and S-theorem are adopted to reconstruct the equivalence of the above formula into a deterministic optimization model as follows:
Figure BDA0002979445520000071
Figure BDA0002979445520000072
Figure BDA0002979445520000073
Figure BDA0002979445520000074
Figure BDA0002979445520000075
further, in the step S5, the specific steps are:
the linearization segment number is set as Λ, [ (B + upsilon)/2] 2 The slope of the line corresponding to the lambda-th segment is
Figure BDA0002979445520000076
Intercept of
Figure BDA0002979445520000077
[(B+Υ)/2] 2 The continuous variable corresponding to the lambda-th segment is
Figure BDA0002979445520000078
0-1 variable selection of [ (B + y)/2 2 ]Piecewise linear corresponding to a straight line of
Figure BDA0002979445520000079
[(B-Υ)/2] 2 The slope of the line corresponding to the lambda-th segment is
Figure BDA00029794455200000710
Intercept of
Figure BDA00029794455200000711
[(B-Υ)/2] 2 The continuous variable corresponding to the lambda segment is
Figure BDA00029794455200000712
The variable 0-1 is selected from [ (B-gamma)/2] 2 Piecewise linear corresponding to a straight line of
Figure BDA00029794455200000713
The calculation formula of (c) is as follows:
Figure BDA00029794455200000714
Figure BDA00029794455200000715
then the piecewise linearization is carried out on the bilinear item y B:
Figure BDA00029794455200000716
Figure BDA0002979445520000081
Figure BDA0002979445520000082
Figure BDA0002979445520000083
order:
Figure BDA0002979445520000084
the reconstructed cone constraint equivalently translates to:
Figure BDA0002979445520000085
the above formula is approximated by a polyhedron:
Figure BDA0002979445520000086
Figure BDA0002979445520000087
the invention has the beneficial effects that:
1. according to the distributed photovoltaic limit grid-connected capacity evaluation method based on the distributed robust optimization, the distributed photovoltaic grid-connected capacity in the power distribution network is maximized to serve as a target function, a fuzzy set of moment uncertainty of distributed photovoltaic output and load requirements is established by introducing constraint conditions such as distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint, node voltage constraint and the like, a distributed photovoltaic limit grid-connected capacity optimization model is reconstructed, and the function of accurately obtaining probability distribution parameters in the distributed photovoltaic limit grid-connected capacity evaluation is achieved.
2. Compared with the deterministic optimization technology, the method effectively tolerates the node voltage out-of-limit risk and has higher robustness;
3. compared with a random optimization method, the method does not need to establish accurate probability distribution, so that the method is more robust when the uncertainty of probability distribution parameters is processed; compared with a robust optimization method, the worst case of probability distribution is considered in the invention rather than the worst scenario, so that the conservative property of the total capacity result of the distributed photovoltaic grid connection is reduced.
4. The method converts the evaluation model into a mixed integer linear programming problem, and has high solving efficiency.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a schematic diagram of an example topology of a 33-node power distribution network according to an embodiment of the present invention.
Fig. 3 is a grid-connected capacity result diagram of each distributed photovoltaic access point according to the embodiment of the present invention.
FIG. 4 is a graph of the trend of the change in the probability of opportunity constrained failure of an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
According to the method, firstly, the distributed photovoltaic grid-connected capacity in a power distribution network is maximized as a target function, and constraint conditions such as distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint, node voltage constraint and the like are considered; and then establishing a fuzzy set of moment uncertainty of distributed photovoltaic output and load demand, considering node voltage and branch transmission capacity out-of-limit opportunity constraints, reconstructing a distributed photovoltaic limit grid-connected capacity optimization model under moment uncertainty input by adopting cone linear dual transformation and S-lemma, and performing piecewise linearization to obtain a mixed integer linear programming model for solving, so that a commercial solver Cplex is conveniently called for solving.
Referring to the topology diagram of fig. 2, an improved IEEE-33 node system is taken as an example. Referring to fig. 1, the distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization according to the embodiment of the present invention includes the following steps:
s1: initializing, and inputting line parameters of an IEEE-33 node power distribution network, distributed photovoltaic output and load prediction reference values; selecting nodes 15, 22, 25 and 32 as alternative nodes accessed to the distributed photovoltaic, taking 1.1 and 0.95 times of reference voltage as upper and lower limits of node voltage for voltage constraint, referring to an IEEE-33 node calculation example for line capacity constraint, and assuming constant power factors of the distributed photovoltaic and load; the errors of the distributed photovoltaic output and load active power requirements relative to the reference value are assumed to be subjected to normal distribution, the mean value of the errors is 0, the standard deviation of the prediction errors is assumed to be 5% of the reference value, and the probability of out-of-limit of node voltage and line transmission capacity is 0.05.
S2: establishing a distribution network limit distributed photovoltaic grid-connected capacity optimization model; taking the maximization of the distributed photovoltaic grid-connected capacity in the power distribution network as a target function, and considering constraint conditions such as distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint, node voltage constraint and the like
S21: the method comprises the following steps of establishing a target function for maximizing the distributed photovoltaic grid-connected capacity in the power distribution network, wherein the target function is shown as the following formula:
Figure BDA0002979445520000101
in the formula: s i For distributed photovoltaic grid-connected capacity at node i, Ψ PV Is a distributed photovoltaic access node set.
S22: the method for establishing the optimization constraint conditions of the distributed photovoltaic grid-connected capacity in the power distribution network comprises the following steps: distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint and node voltage constraint are sequentially explained as follows.
(1) Distributed photovoltaic operation constraints:
Figure BDA0002979445520000102
in the formula:
Figure BDA0002979445520000103
distributing photovoltaic actual output active power and reactive power for the node i at the moment t respectively;
Figure BDA0002979445520000104
for node i the distributed photovoltaic power conversion coefficient during time t,
Figure BDA0002979445520000105
and (4) the power factor of the distributed photovoltaic at the time t for the node i. And T is a distributed photovoltaic grid-connected capacity evaluation period.
(2) Node power balance constraint:
Figure BDA0002979445520000106
in the formula:
Figure BDA0002979445520000107
the node i is subjected to actual active power and reactive power requirements at the moment t; p ij,t 、Q ij,t Respectively representing the active power and the reactive power of a branch ij flowing from a node i to a node j at the moment t; Ψ n And gathering all nodes of the power distribution network.
(3) And (3) power flow constraint: describing the power flow constraint of the power distribution network by using a Distflow branch power flow model, which is shown as the following formula:
Figure BDA0002979445520000111
in the formula: v i,t Is the voltage amplitude of node i at time t, U i,t Is the square of the voltage amplitude of the node i at the time t; Ψ b All branches in the power distribution network are collected; r is ij And x ij The resistance and reactance values of branch ij, respectively. Defining the square L of the magnitude of the current of the branch with the new variable ij,t Comprises the following steps:
Figure BDA0002979445520000112
after relaxation, two three-dimensional second-order cones can be jointly represented:
Figure BDA0002979445520000113
Figure BDA0002979445520000114
in the formula u ij,t Is an introduced virtual intermediate variable. Let K =1,2, \ 8230, K, K is the number of facets, generally 11 is taken to satisfy the approximate precision of the second order cone; let a k 、b k 、m k 、n k The virtual variables introduced for the polyhedron linearization are further approximated by a polyhedron as shown in the following formula:
Figure BDA0002979445520000115
Figure BDA0002979445520000116
i.e. the flow equation constraints are:
Figure BDA0002979445520000121
(4) branch transmission capacity constraint:
Figure BDA0002979445520000122
in the formula: s ij,max For the maximum transmission capacity of a branch ij, the branch transmission capacity constraint is a conical constraint, or the sameThe sample can be approximated by a polyhedron norm, as shown in the following equation:
Figure BDA0002979445520000123
(5) node voltage constraint:
Figure BDA0002979445520000124
in the formula of U i,max 、U i,min Respectively, the upper and lower bounds of the square of the node voltage amplitude.
Figure BDA0002979445520000125
S3: establishing a moment uncertainty fuzzy set of distributed photovoltaic and load; introducing random variables
Figure BDA0002979445520000126
To define the actual power conversion coefficient of the distributed photovoltaic
Figure BDA0002979445520000128
And load active power and reactive power
Figure BDA0002979445520000127
As shown in the following formula:
Figure BDA0002979445520000131
under the condition that accurate zeta probability distribution information is difficult to acquire, the information of the first moment and the second moment of a random variable zeta can be counted through limited historical data, and a zeta fuzzy set based on moment uncertainty is defined as the following formula:
Figure BDA0002979445520000132
in the formula, f (xi) is xiIs a function of the probability density of, S ∈ R 2 Is a supporting set of probability density functions f (ξ);
Figure BDA0002979445520000133
is a random variable
Figure BDA0002979445520000134
The first order moment confidence interval of (a) is,
Figure BDA0002979445520000135
is a random variable
Figure BDA0002979445520000136
First order moment confidence interval of (1);
Figure BDA0002979445520000137
is a random variable
Figure BDA0002979445520000138
The second-order moment confidence interval of (a),
Figure BDA0002979445520000139
is a random variable
Figure BDA00029794455200001310
Second order moment confidence interval.
S4: reconstructing node voltage and branch transmission capacity out-of-limit opportunity constraint conditions; the invention considers node voltage and branch transmission capacity out-of-limit opportunity constraints as shown in the following formula:
Pr{U i,min ≤U i,t ≤U i,max }≥1-ε
Figure BDA00029794455200001311
wherein epsilon is an opportunity constraint confidence parameter and represents that the probability of node voltage and branch transmission capacity exceeding the limit is lower than epsilon. The opportunity constraint conditions are uniformly expressed as:
Pr{A T ξ≤B}≥1-ε
wherein A = [ A ] 1 ,A 2 ]Are affine coefficients. On the basis of considering the moment uncertain fuzzy set established in the third step, the opportunity constraint condition is converted into
Figure BDA00029794455200001312
The left side of the above formula is given Pr { A T ξ ≦ B } a worst case probability bound on the fuzzy set D, equivalent to the target value of the following optimization problem:
Figure BDA0002979445520000141
Figure BDA0002979445520000142
Figure BDA0002979445520000143
Figure BDA0002979445520000144
in the formula II c (xi) is an indicator function, i.e. decision A T Xi is less than or equal to B, if A is T B is less than or equal to xi, pi c And (ξ) is 1, and vice versa is 0. And equivalently reconstructing the above formula into a deterministic optimization model by using the dual transformation of cone linearity and S-lemma:
Figure BDA0002979445520000145
Figure BDA0002979445520000146
Figure BDA0002979445520000147
Figure BDA0002979445520000148
Figure BDA0002979445520000149
in the above formula, q,
Figure BDA00029794455200001410
α n 、β n And upsilon ≧ 0 is dual variable.
S5: and linearizing the fourth step to establish a constraint condition after reconstruction, and linearizing the nonlinear constraint after reconstruction. Mainly, the piecewise linearization of the bilinear term γ B was as follows:
Figure BDA00029794455200001411
Figure BDA00029794455200001412
Figure BDA00029794455200001413
Figure BDA0002979445520000151
wherein Λ is the number of linearization segments,
Figure BDA0002979445520000152
represents [ (B + y)/2] 2 The slope and intercept of the line corresponding to the lambda segment,
Figure BDA0002979445520000153
represents [ (B + y)/2] 2 The continuous variable corresponding to the lambda-th segment,
Figure BDA0002979445520000154
represents the 0-1 variable choice [ (B + y)/2] 2 Piecewise linear corresponding straight lines;
Figure BDA0002979445520000155
represents [ (B-upsilon)/2] 2 The slope and intercept of the line corresponding to the lambda segment,
Figure BDA0002979445520000156
represents [ (B-y)/2] 2 The continuous variable corresponding to the lambda-th segment,
Figure BDA0002979445520000157
represents the variable selection of 0-1 [ (B-gamma)/2] 2 Piecewise linear corresponds to a straight line.
Figure BDA0002979445520000158
The calculation formula of (a) is as follows:
Figure BDA0002979445520000159
Figure BDA00029794455200001510
further order
Figure BDA00029794455200001511
The reconstructed cone constraint can be equivalently converted into
Figure BDA00029794455200001512
The above formula is further approximated by a polyhedron
Figure BDA0002979445520000161
Figure BDA0002979445520000162
S6: and calling a commercial solver Cplex to solve the mixed integer linear programming model which is established and converted in the first five steps, and outputting the distributed photovoltaic limit grid-connected capacity, as shown in FIG. 3.
Compared with the traditional random optimization method and the robust optimization method, the distributed robust optimization photovoltaic grid-connected capacity evaluation method is provided, and the total distributed photovoltaic grid-connected capacity is shown in table 1.
Table 1 distributed photovoltaic grid-connected total capacity comparison table
Method Total grid-connected Capacity (MW)
Stochastic optimization 3.571
Robust optimization 3.161
Distributed robust optimization 3.496
As can be easily found from table 1 and fig. 3, the total photovoltaic grid-connected capacity based on the distributed robust optimization is more conservative than that based on the random optimization method, but the conservative property is greatly reduced compared with the robust optimization method. The reason for the above difference is that the stochastic optimization method only considers the case under the empirical distribution and ignores the uncertainty of the probability distribution parameters, whereas the robust optimization method does not utilize the probability distribution information at all and only considers the worst case, resulting in very conservative results.
Fig. 4 compares the influence of the prediction error standard deviation and the chance constraint inequality failure probability of the distributed photovoltaic output and load active power demand on the distributed photovoltaic grid-connected total capacity result. As shown in fig. 4, under the condition of a certain standard deviation, the distributed photovoltaic grid-connected total capacity gradually increases with the increase of the probability of failure of the opportunity constraint inequality, because the probability of failure of the opportunity constraint inequality is greater, that is, the probability of out-of-limit of the allowed node voltage and the line transmission capacity is greater, the constraint condition limit is obviously weakened, so that the photovoltaic grid-connected capacity of the power distribution network is increased. In addition, the larger the standard deviation of the prediction error is, the larger the range of the probability distribution function set contained in the fuzzy set is, and the distribution robust optimization method selects the worst probability distribution from the probability distribution function set for decision making, so that the standard deviation of the prediction error is increased, and the photovoltaic grid-connected total quantity result of the power distribution network is more conservative.
The above embodiments are only used for illustrating the design idea and features of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the content of the present invention and implement the present invention accordingly, and the protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes and modifications made in accordance with the principles and concepts disclosed herein are intended to be included within the scope of the present invention.

Claims (7)

1. The distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization is characterized by comprising the following steps: the method comprises the following steps:
s1: initializing, inputting power distribution network line parameters, distributed photovoltaic output and load prediction reference values;
s2: establishing a distribution network limit distributed photovoltaic grid-connected capacity optimization model; taking the maximization of distributed photovoltaic grid-connected capacity in a power distribution network as a target function, and introducing constraint conditions including distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint and node voltage constraint;
s3: establishing a moment uncertainty fuzzy set of distributed photovoltaic output and load requirements;
the method comprises the following specific steps:
let the distributed photovoltaic power conversion coefficient of the node i in the t period be
Figure FDA0003797788290000011
The actual active power demand of the load of the node i at the moment t is set as
Figure FDA0003797788290000012
The reactive power requirement is
Figure FDA0003797788290000013
Introducing random variables
Figure FDA0003797788290000014
Defining distributed photovoltaic actual power conversion coefficients
Figure FDA0003797788290000015
And load active power and load reactive power
Figure FDA0003797788290000016
Comprises the following steps:
Figure FDA0003797788290000017
let the probability density function of xi be f (xi), and the support set of the probability density function f (xi) be S ∈ R 2 (ii) a Random variable
Figure FDA0003797788290000018
Is a first order moment confidence interval of
Figure FDA0003797788290000019
Random variable
Figure FDA00037977882900000110
Has a first moment confidence interval of
Figure FDA00037977882900000111
Random variable
Figure FDA00037977882900000112
The second order moment confidence interval of
Figure FDA00037977882900000113
Random variable
Figure FDA00037977882900000114
The second order moment confidence interval of
Figure FDA00037977882900000115
Under the condition that accurate probability distribution information of the random variable xi is difficult to obtain, counting first moment information and second moment information of the random variable xi through limited historical data, and defining a xi fuzzy set based on moment uncertainty as follows:
Figure FDA00037977882900000116
s4: reconstructing node voltage and branch transmission capacity out-of-limit opportunity constraint conditions;
the method comprises the following specific steps: setting an opportunity constraint confidence parameter as epsilon, and representing that the probability of node voltage and branch transmission capacity out-of-limit is lower than epsilon; the out-of-limit opportunity constraints of the node voltage and the branch transmission capacity are as follows:
Pr{U i,min ≤U i,t ≤U i,max }≥1-ε，
Pr{-S ij,max ≤cos(lφ)P ij,t +sin(lφ)Q ij,t ≤S ij,max }≥1-ε，
Figure FDA0003797788290000021
let affine coefficient be A = [ A = 1 ,A 2 ]The opportunity constraint conditions are collectively expressed as:
Pr{A T ξ≤B}≥1-ε；
converting the chance constraint condition into the chance constraint condition on the basis of the moment uncertainty fuzzy set established in the step S3
Figure FDA0003797788290000022
The left side of the above formula gives Pr { A T ξ ≦ B } the worst case probability bound on the fuzzy set D, equivalent to the target value of the following optimization problem:
Figure FDA0003797788290000023
Figure FDA0003797788290000024
Figure FDA0003797788290000025
Figure FDA0003797788290000026
in which an indication function pi is arranged c (xi) use in judgment A T B is less than or equal to xi; if A T Xi is less than or equal to B, if B is true, pi c (xi) is 1, if A T Xi is less than or equal to B, if B is not established, pi c (xi) is 0; q is set,
Figure FDA0003797788290000027
α n 、β n And upsilon is more than or equal to 0 and is a dual variable, and the dual transformation of cone linearity and S-theorem are adopted to reconstruct the equivalent of the above formula into a deterministic optimization model as follows:
Figure FDA0003797788290000028
Figure FDA0003797788290000029
Figure FDA00037977882900000210
Figure FDA00037977882900000211
Figure FDA0003797788290000031
s5: linearizing the constraint condition reconstructed in the step S4;
the method comprises the following specific steps:
let the linearization segment number be Λ, [ (B + upsilon)/2] 2 The slope of the line corresponding to the lambda-th segment is
Figure FDA0003797788290000032
Intercept of
Figure FDA0003797788290000033
[(B+Υ)/2] 2 The continuous variable corresponding to the lambda segment is
Figure FDA0003797788290000034
0-1 variable selection of [ (B + y)/2] 2 Piecewise linear corresponding to a straight line of
Figure FDA0003797788290000035
[(B-Υ)/2] 2 The slope of the line corresponding to the lambda-th segment is
Figure FDA0003797788290000036
Intercept of
Figure FDA0003797788290000037
[(B-Υ)/2] 2 The continuous variable corresponding to the lambda segment is
Figure FDA0003797788290000038
The variable 0-1 is selected from [ (B-gamma)/2] 2 Piecewise linear corresponding to a straight line of
Figure FDA0003797788290000039
The calculation formula of (a) is as follows:
Figure FDA00037977882900000310
Figure FDA00037977882900000311
then the piecewise linearization is carried out on the bilinear item y B:
Figure FDA00037977882900000312
Figure FDA00037977882900000313
Figure FDA00037977882900000314
Figure FDA00037977882900000315
order:
Figure FDA00037977882900000316
the reconstructed cone constraint equivalently translates to:
Figure FDA0003797788290000041
let a k 、b k 、m k 、n k For the virtual variables introduced for polyhedron linearization, the polyhedron approximation adopted for the above formula is:
Figure FDA0003797788290000042
Figure FDA0003797788290000043
s6: and (5) solving the mixed integer linear programming model established and converted in the steps S1 to S5 through a commercial solver, and outputting the distributed photovoltaic limit grid-connected capacity.
2. The distributed robust optimization-based distributed photovoltaic limit grid-connected capacity evaluation method according to claim 1, characterized in that: in the step S2, the specific steps are as follows:
s21: setting distributed photovoltaic grid-connected capacity at node i as S i The distributed photovoltaic access node set is psi PV Maximizing the distributed photovoltaic grid-connected capacity in the power distribution network as a target function:
Figure FDA0003797788290000044
s22: the constraint conditions introduced for optimizing the distributed photovoltaic grid-connected capacity in the power distribution network comprise: distributed photovoltaic operation constraint, node power balance constraint, power flow constraint, branch transmission capacity constraint and node voltage constraint.
3. The distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization according to claim 2, characterized in that: in the step S22, the actual distributed photovoltaic output active power of the node i at the time t is set as
Figure FDA0003797788290000045
Reactive power of
Figure FDA0003797788290000046
The distributed photovoltaic power conversion coefficient of the node i in the t period is
Figure FDA0003797788290000047
The power factor of the distributed photovoltaic of the node i in the period t is
Figure FDA0003797788290000048
And if the evaluation period of the distributed photovoltaic grid-connected capacity is T, the distributed photovoltaic operation constraint is as follows:
Figure FDA0003797788290000051
4. the distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization according to claim 3, characterized in that: in the step S22, the actual active power demand of the load of the node i at the time t is set as
Figure FDA0003797788290000052
The reactive power requirement is
Figure FDA0003797788290000053
The active power of the branch ij flowing from the node i to the node j at the moment t is P ij,t And the reactive power is Q ij,t (ii) a The set of all nodes of the power distribution network is psi n Then the node power balance constraint is:
Figure FDA0003797788290000054
5. the distributed robust optimization-based distributed photovoltaic limit grid-connected capacity evaluation method according to claim 4, characterized in that: in step S22, the maximum transmission capacity of the branch ij is set as S ij,max Then the branch transmission capacity constraint is:
Figure FDA0003797788290000055
at this moment, the branch transmission capacity constraint is a cone constraint, and the polyhedron norm is adopted to be approximately:
Figure FDA0003797788290000056
6. the distributed robust optimization-based distributed photovoltaic limit grid-connected capacity evaluation method according to claim 4, characterized in that: in step S22, the voltage amplitude of the node i at time t is set as V i,t Square of voltage amplitude is U i,t All branches in the distribution network are grouped into psi b The resistance of branch ij is r ij Reactance value x ij Then, the flow constraint is described as follows by using a Distflow branch flow model:
Figure FDA0003797788290000057
defining the square L of the magnitude of the current of the branch with the new variable ij,t Comprises the following steps:
Figure FDA0003797788290000061
let the introduced virtual intermediate variable be u ij,t After the above formula is relaxed, the above formula is jointly expressed as:
Figure FDA0003797788290000062
Figure FDA0003797788290000063
let K =1,2, \ 8230, K, K is the number of facets, let a k 、b k 、m k 、n k The virtual variables introduced for polyhedron linearization are approximated by adopting a polyhedron as follows:
Figure FDA0003797788290000064
Figure FDA0003797788290000065
the flow constraint equation is:
Figure FDA0003797788290000071
Figure FDA0003797788290000072
Figure FDA0003797788290000073
7. the distributed photovoltaic limit grid-connected capacity evaluation method based on distributed robust optimization according to claim 6, characterized in that: in the step S22, the upper bound of the square of the node voltage amplitude is set to U i,max The lower boundary is U i,min ，U i,t ＝U ref ,
Figure FDA0003797788290000074
The node voltage constraint is then:
U i,min ≤U i,t ≤U i,max ，
Figure FDA0003797788290000075
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