CN111900715B - Power distribution network optimal scheduling method considering random output of high-density distributed power supply - Google Patents

Power distribution network optimal scheduling method considering random output of high-density distributed power supply Download PDF

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CN111900715B
CN111900715B CN202010525322.3A CN202010525322A CN111900715B CN 111900715 B CN111900715 B CN 111900715B CN 202010525322 A CN202010525322 A CN 202010525322A CN 111900715 B CN111900715 B CN 111900715B
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CN111900715A (en
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李静
李艳君
肖铎
杜鹏英
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Hangzhou City University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/003—Load forecast, e.g. methods or systems for forecasting future load demand
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/28—Arrangements for balancing of the load in a network by storage of energy
    • H02J3/32—Arrangements for balancing of the load in a network by storage of energy using batteries with converting means
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/466—Scheduling the operation of the generators, e.g. connecting or disconnecting generators to meet a given demand
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/22—The renewable source being solar energy
    • H02J2300/24—The renewable source being solar energy of photovoltaic origin
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/40—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation wherein a plurality of decentralised, dispersed or local energy generation technologies are operated simultaneously
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/70—Wind energy
    • Y02E10/76—Power conversion electric or electronic aspects

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Abstract

The invention discloses a power distribution network optimal scheduling method considering random output of a high-density distributed power supply, which models the random time sequence characteristic of wind and light distributed power supplies injecting power into a power grid node and samples a random power flow space based on a sparse grid point matching theory; aiming at reducing the active loss and the node voltage deviation of the power distribution network, establishing a power distribution network active and reactive power combined random optimization model containing power flow balance and opportunity constraint; and finally, performing orthogonal polynomial approximation on a random space in the active and reactive power scheduling problem based on a spectral decomposition method, establishing a convex approximation certainty optimization model equivalent to the random optimization model, and approximating the optimal solution of the random space by using a sample set composed of sparse nodes, so that the approximation precision of understanding is ensured, and the dimension disaster of the active and reactive power combined optimization scheduling model of the power distribution network in a high-dimensional random parameter space is avoided. The method can be widely applied to optimal scheduling of the power distribution network under the influence of high-dimensional random factors, and the power quality of the power distribution network is improved.

Description

Power distribution network optimal scheduling method considering random output of high-density distributed power supply
Technical Field
The invention belongs to the technical field of power system optimization, and particularly relates to a power distribution network active and reactive power combined optimization scheduling method considering high-dimensional randomness and opportunity constraint.
Background
Due to the large uncertainty of distributed power sources such as wind energy, solar energy, etc., new challenges are faced in the operation and control of power systems containing a high percentage of new energy. The random optimization scheduling technology of the power system is researched, and the minimum active loss of a power grid can be realized while the voltage deviation of a node of a power distribution network is ensured to be improved under a random environment. In order to overcome the complexity of a large number of distributed power supplies and a high-dimensional random parameter processing technology, the influence of random parameters on an electric power system is analyzed by adopting an effective uncertainty quantification means, an equivalent deterministic convex optimization model is established, and the method has important significance for the research of high-density distributed power supply optimization scheduling and power distribution network electric energy quality improvement.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a power distribution network active and reactive power combined optimization scheduling method considering the random output of a high-density distributed power supply by utilizing orthogonal polynomial approximation of a high-dimensional random space and a sparse grid point matching method.
In order to achieve the purpose, the invention provides a power distribution network optimal scheduling method considering random output of a high-density distributed power supply, which comprises the following specific steps:
s1: and establishing a low-order approximate model for simulating the random time sequence characteristics of the output of the distributed power supply by using a Karhunen-Loeve expansion representation method.
The random timing characteristic of the output of the analog distributed power supply comprises the following steps:
s1.1: due to the random fluctuation of the output of the wind power and the solar photovoltaic power supply, the injection power of the distributed power supply access node of the power distribution network at any moment t can be regarded as a random variable, and the random process is formed by the expansion of the random variable in the time dimension. The injected power at distribution network node i at time t is described as:
Figure GDA0003659270430000011
Figure GDA0003659270430000012
in the formula (I), the compound is shown in the specification,
Figure GDA0003659270430000013
and
Figure GDA0003659270430000014
the active and reactive power output predicted values which are injected at the node i at the moment t are shown;
Figure GDA0003659270430000015
representing a node generator set, wherein WT is fan output of node injection, PV is photovoltaic output of node injection, and B is battery output of a node;
Figure GDA0003659270430000016
and
Figure GDA0003659270430000017
representing the active and reactive load predicted values at the node i at the time t;
Figure GDA0003659270430000018
representing a random variable;
Figure GDA0003659270430000021
and
Figure GDA0003659270430000022
and the active and reactive prediction errors at the node i at the time t are represented, and the prediction errors belong to a Gaussian random process under the assumption that the random characteristics of the errors at any time t meet normal distribution.
S1.2: a Karhunen-Loeve expansion of the stochastic process was established and truncated by taking the top N terms as follows:
Figure GDA0003659270430000023
Figure GDA0003659270430000024
in which N is the order of truncation xi n Are random variables that are not related to each other,
Figure GDA0003659270430000025
and
Figure GDA0003659270430000026
respectively, a random process correlation function C pp The characteristic value and the characteristic function of (c),
Figure GDA0003659270430000027
and
Figure GDA0003659270430000028
respectively random process correlation function C qq The characteristic value and the characteristic function satisfy:
Figure GDA0003659270430000029
Figure GDA00036592704300000210
where T is the grid operating period, T 1 And t 2 Respectively representing different time coordinates; the correlation function of the gaussian random process is sampled in exponential form:
Figure GDA00036592704300000211
in the formula I p And l q The correlation lengths of the active and reactive prediction error random processes are respectively expressed.
S2: aiming at improving the quality of electric energy, establishing a power distribution network active and reactive power combined random optimization model containing power flow balance and opportunity constraint according to distributed power sources and load parameters, and concretely, the method comprises the following steps;
s2.1: the objective of the optimized dispatching is that the expected value of the active network loss in the power grid operation period T is minimum, namely
Figure GDA00036592704300000212
In the formula, E2]Represents a mathematical expectation;
Figure GDA00036592704300000213
Figure GDA00036592704300000214
an active network loss model on the power grid direct current tide; i denotes a node set of the distribution network, G ij Representing the real part of the ith row and j column elements of the nodal admittance matrix,
Figure GDA00036592704300000215
and
Figure GDA00036592704300000216
representing the node voltage magnitude at time t for grid node i and node j.
S2.2: the method comprises the following steps of establishing a constraint condition of an active and reactive combined random optimization model of the power distribution network, and specifically comprising the following steps:
s2.2.1: stochastic power flow constraint
Figure GDA00036592704300000217
Figure GDA00036592704300000218
In the formula, G ij And B ij Respectively a real part and an imaginary part of j columns of elements in the ith row of the node admittance matrix;
Figure GDA0003659270430000031
and
Figure GDA0003659270430000032
the amplitude and the phase angle of the j-th node voltage at the time t are respectively represented, and the node voltage and the amplitude are random variables due to the influence of random parameters of the node injection power. Trend aboutRandom input parameters in bundles
Figure GDA0003659270430000033
And
Figure GDA0003659270430000034
as shown in equations (3) to (4).
S2.2.2: battery charge and discharge power and capacity constraints
Figure GDA0003659270430000035
Figure GDA0003659270430000036
Figure GDA0003659270430000037
Figure GDA0003659270430000038
In the formula (I), the compound is shown in the specification,
Figure GDA0003659270430000039
representing the amount of stored energy of a battery installed at the i-node at time t, at representing the time span from t-1 to t, p b Which shows the charge-discharge efficiency of the battery,
Figure GDA00036592704300000310
and
Figure GDA00036592704300000311
respectively represent the lower limit and the upper limit of the charge-discharge power of a battery installed at the i-node (wherein
Figure GDA00036592704300000312
Which represents the maximum discharge power of the storage battery,
Figure GDA00036592704300000313
representing the maximum charging power of the battery),
Figure GDA00036592704300000314
and
Figure GDA00036592704300000315
respectively representing a lower limit and an upper limit of the amount of stored electricity of a battery installed at the i-node,
Figure GDA00036592704300000316
representing the reactive power supplied by the battery grid-connected converter at time t,
Figure GDA00036592704300000317
representing the capacity of the battery-connected converter at node i.
S2.2.3 distributed power supply active and reactive power output constraints
Figure GDA00036592704300000318
In the formula (I), the compound is shown in the specification,
Figure GDA00036592704300000319
and
Figure GDA00036592704300000320
and respectively representing the upper limit of the active power output of the ith distributed power supply and the maximum capacity of the grid-connected converter.
S2.2.4: security opportunity constraints
Figure GDA00036592704300000321
Figure GDA00036592704300000322
Wherein pr { } denotes in bracesProbability of equality being true;
Figure GDA00036592704300000323
and
Figure GDA00036592704300000324
respectively the allowable upper and lower limits of the voltage fluctuation at node i,
Figure GDA00036592704300000325
and
Figure GDA00036592704300000326
respectively represents the upper limit and the lower limit of the active power fluctuation of the branch transmission, 0.5<η<1 indicates that the opportunity constraint event is a large probability event.
S3: orthogonal polynomial approximation is carried out on a random space in the power distribution network active and reactive power combined random optimization problem based on a spectral decomposition method, the random power flow space is sampled based on a sparse grid distribution point theory, a convex approximation certainty optimization model equivalent to the random optimization model is established,
s3.1, expanding and approaching random power flow state variables by using a chaotic polynomial (gPC), and then in the random optimization scheduling model of the power distribution network active and reactive power combination established in the step S2, obtaining the random power flow state variables
Figure GDA0003659270430000041
And
Figure GDA0003659270430000042
the K-th order gPC approximation polynomial of (a) is described as:
Figure GDA0003659270430000043
Figure GDA0003659270430000044
in the formula, K is the number of terms of polynomial expansion,
Figure GDA0003659270430000045
is the basis function of the kth term of the orthogonal polynomial,
Figure GDA0003659270430000046
and
Figure GDA0003659270430000047
and the approximation coefficient corresponding to the k-th term base function. The orthogonal polynomial basis function satisfies the following orthogonal property,
Figure GDA0003659270430000048
in the formula, E2]The mathematical expectation is represented by the mathematical expectation,
Figure GDA0003659270430000049
is a basis function of the nth term of the orthogonal polynomial,
Figure GDA00036592704300000410
to normalize constant, δ nk Is a Kronecker operator, and is a Kronecker operator,
Figure GDA00036592704300000411
as a random variable
Figure GDA00036592704300000412
Is determined.
S3.2 establishing an opportunity-constrained deterministic convex approximation model based on a spectral method, for opportunity constraint
Figure GDA00036592704300000413
Available from the Cantelli's inequality, an equivalent of the following opportunistic constraints
Figure GDA00036592704300000414
In the formula, Var [ ] represents the variance of a random variable.
According to S3.1, the random variable can be approximated by a Kth-order gPC approximation polynomial, and the mean value of the node voltage can be known according to the orthogonal property of the orthogonal polynomial basis function
Figure GDA00036592704300000415
Sum variance
Figure GDA00036592704300000416
Can be approximated by a polynomial coefficient,
Figure GDA00036592704300000417
Figure GDA00036592704300000418
substituting (23) and (24) into the above inequality (22) yields the convex equivalent of the opportunity constraint (21):
Figure GDA00036592704300000419
as can be seen, equation (25) relates to the gPC approximation coefficients
Figure GDA00036592704300000420
Is convex. The opportunity constraints (16) to (17) in the original active reactive power joint random optimization problem are equivalent to:
Figure GDA0003659270430000051
s3.3: for N-dimensional random input variables
Figure GDA0003659270430000052
The sparse node sample set is constructed by utilizing Smolyak algorithm
Figure GDA0003659270430000053
And weight set of corresponding sparse node
Figure GDA0003659270430000054
Solving a deterministic power flow equation at each sample point to obtain a corresponding deterministic power flow equation,
Figure GDA0003659270430000055
Figure GDA0003659270430000056
Figure GDA0003659270430000057
solving the coefficients of the k-order gPC expansions (18) and (19) by using a discrete Galerkin projection method based on sparse nodes,
Figure GDA0003659270430000058
Figure GDA0003659270430000059
in the formula, σ m Representing sparse nodes
Figure GDA00036592704300000510
The corresponding weight.
The deterministic convex approximation optimization model for the random optimization scheduling of the power distribution network can be obtained, and is shown in formulas (8), (11) to (15), (18), (19) and (26) to (30). And solving the convex optimization problem according to the deterministic convex approximation optimization model of the distribution network random optimization scheduling to obtain the distribution network optimization scheduling result.
Further, in step S3.1, different basis functions may be selected according to the distribution characteristics of the random variables.
Further, in step S3.3, the convex optimization problem is solved by using optimization tool boxes MOSEK, CVX, and the like, and a solution of the active and reactive power joint optimization scheduling of the power distribution network including the high-density distributed power supply is obtained.
The invention has the beneficial effects that: the number of samples obtained by the high-dimensional random space sparse node is much smaller than that of tensor product nodes, and the dimensionality disaster is relieved to a certain extent. In addition, opportunity constraint describes out-of-limit probability limit of node voltage of the power distribution network, actual operation requirements of the power distribution network with the high-density distributed power supply are met better, and feasibility of an active and reactive combined scheduling scheme is guaranteed. The number of sample points required by the traditional Monte Carlo method is too large, the sample points exponentially rise along with the increase of the dimension, the calculation amount is very large, and dimension disasters can be met on the aspect of processing high-dimensional random parameters. Aiming at the defect, the deterministic convex equivalence model for the random optimization scheduling problem is provided based on a spectral decomposition approximation method. A sample set formed by sparse nodes is used for approaching the optimal solution of the random space, so that the approaching precision of the understanding is ensured, and the dimension disaster of the active and reactive power combined random optimization scheduling model of the power distribution network in the high-dimensional random parameter space is avoided.
Drawings
FIG. 1 is a flow chart of the steps of the present invention;
FIG. 2 is a 33-node power distribution network containing a new energy source;
FIG. 3 is a Gaussian process K-L unfolding simulation.
Detailed Description
In order to express the idea of the present invention more clearly and intuitively, the following further introduces the technical solution of the present invention with reference to the specific embodiments. As shown in fig. 2, in an active and reactive joint scheduling method for a 33-node power distribution network with a high-proportion distributed power supply, nodes 4,6,7,14,16,20,24,25,30 and 32 in the power distribution network are respectively connected with wind and light distributed power supplies.
As shown in fig. 1, the technical scheme specifically includes the following steps:
s1: and establishing a low-order approximate model for simulating the random time sequence characteristics of the output of the distributed power supply by using an orthogonal series expansion representation method.
Further, in step S1, the step of simulating the random timing characteristic of the distributed power output includes the following steps:
s1.1: due to the random fluctuation of the output of the wind power and the solar photovoltaic power supply, the injection power of the distributed power supply access node of the power distribution network at any moment t is regarded as a random variable, and the random process is formed by the expansion of the random variable in the time dimension. For the present case, the injection power at time t for node i ∈ {4,6,7,14,16,20,24,25,30,32} is:
Figure GDA0003659270430000061
Figure GDA0003659270430000062
in the formula (I), the compound is shown in the specification,
Figure GDA0003659270430000063
and
Figure GDA0003659270430000064
the active and reactive power output predicted values which are injected at the node i at the moment t are shown;
Figure GDA0003659270430000065
representing a node generator set, wherein WT is fan output of node injection, PV is photovoltaic output of node injection, and B is battery output of a node;
Figure GDA0003659270430000066
and
Figure GDA0003659270430000067
representing the active and reactive load predicted values at the node i at the time t;
Figure GDA0003659270430000068
representing a random variable;
Figure GDA0003659270430000069
and
Figure GDA00036592704300000610
and (3) representing active and reactive prediction errors at a node i at the time t, and fitting the random fluctuation characteristics of the prediction errors by using standard Gaussian distribution.
S1.2: c in the form of the following index pp (t 1 ,t 2 ) Describe gaussian random process correlation function:
Figure GDA00036592704300000611
in the formula I p And l q Respectively representing the correlation lengths, t, of the active and reactive prediction error stochastic processes 1 And t 2 Respectively, representing different time coordinates. The scheduling period is divided into 24 time points t 1 ,…,t 24 Get the 24 x 24 correlation matrix C of the random process pp (C qq ) And performing principal component analysis on the matrix, and taking the characteristic value with 5 items in the top
Figure GDA00036592704300000612
And a characteristic function
Figure GDA00036592704300000613
Figure GDA0003659270430000071
Figure GDA0003659270430000072
A Karhunen-Loeve (K-L) expansion of the stochastic process was established and the top 5 truncations taken as follows:
Figure GDA0003659270430000073
Figure GDA0003659270430000074
in the formula
Figure GDA0003659270430000075
Are random variables that are not correlated with each other, so in this case 5-dimensional random variables are used to simulate the random process.
As shown in fig. 3, selecting K-L expansion when N is 5 to simulate the random process of random scheduling input, the left graph is the prediction error Sample value, the right graph is the fitting effect comparison when t is 18, wherein KLE is the probability distribution situation of the K-L model, Sample is the probability distribution situation of the Sample data statistics, PDF represents a standard gaussian distribution curve, and the three are very close to each other, so that the rationality of prediction error random distribution by gaussian distribution fitting and the rationality of 5-order K-L expansion fitting can be seen.
S2: aiming at improving the quality of electric energy, taking multidimensional random parameters such as distributed power supplies, loads and the like into consideration, and establishing a power distribution network active and reactive power combined random optimization model containing power flow balance and opportunity constraint, the method comprises the following steps:
s2.1: the objective of the optimized dispatching is that the expected value of the power grid loss within the grid operation period T-24 is minimum, namely
Figure GDA0003659270430000076
In the formula, E2]Represents a mathematical expectation;
Figure GDA0003659270430000077
Figure GDA0003659270430000078
an active network loss model on the power grid direct current tide; i33 denotes a 33-node distribution network node set selected in this case, G ij Representing the real part of the ith row and j column elements of the nodal admittance matrix,
Figure GDA0003659270430000079
and
Figure GDA00036592704300000710
representing the node voltage magnitude at time t for grid node i and node j.
S2.2: establishing a constraint condition of an active and reactive combined random optimization model of the power distribution network, wherein the steps comprise the following steps:
s2.2.1: stochastic load flow constraints
Figure GDA00036592704300000711
Figure GDA00036592704300000712
In the formula (I); g ij And B ij Respectively a real part and an imaginary part of j columns of elements in the ith row of the node admittance matrix;
Figure GDA00036592704300000713
and
Figure GDA00036592704300000714
the amplitude and the phase angle of the j-th node voltage at the time t are respectively represented, and the node voltage and the amplitude are random variables due to the influence of random parameters of the node injection power. Random input parameters in tidal current constraints
Figure GDA00036592704300000715
And
Figure GDA00036592704300000716
as shown in equations (6) to (7).
S2.2.2: battery charge and discharge power and capacity constraints
Figure GDA00036592704300000717
Figure GDA0003659270430000081
Figure GDA0003659270430000082
Figure GDA0003659270430000083
In the formula (I), the compound is shown in the specification,
Figure GDA0003659270430000084
representing the amount of stored energy of a battery installed at the i-node at time t, at representing the time span from t-1 to t, p b Which shows the charge-discharge efficiency of the battery,
Figure GDA0003659270430000085
and
Figure GDA0003659270430000086
respectively represent the lower limit and the upper limit of the charge-discharge power of a battery installed at the i-node (wherein
Figure GDA0003659270430000087
Which represents the maximum discharge power of the storage battery,
Figure GDA0003659270430000088
representing the maximum charging power of the battery),
Figure GDA0003659270430000089
and
Figure GDA00036592704300000810
respectively representing a lower limit and an upper limit of the amount of stored electricity of a battery installed at the i-node,
Figure GDA00036592704300000811
representing the reactive power supplied by the battery grid-connected converter at time t,
Figure GDA00036592704300000812
representing the capacity of the battery-connected converter at node i.
S2.2.3 distributed power supply active and reactive power output constraints
Figure GDA00036592704300000813
In the formula (I), the compound is shown in the specification,
Figure GDA00036592704300000814
and
Figure GDA00036592704300000815
and respectively representing the upper limit of the active power output of the ith distributed power supply and the maximum capacity of the grid-connected converter.
S2.2.4: security opportunity constraints
Figure GDA00036592704300000816
Figure GDA00036592704300000817
In the formula, pr { } represents the probability of the inequality in braces being true;
Figure GDA00036592704300000818
and
Figure GDA00036592704300000819
respectively the allowable upper and lower limits of the voltage fluctuation at node i,
Figure GDA00036592704300000820
and
Figure GDA00036592704300000821
the upper limit and the lower limit of the active power fluctuation of the branch transmission are respectively represented, and eta is 0.95 to represent that the opportunity constraint event is an approximate rate event.
Therefore, the established power and reactive power combined random optimization scheduling model of the power distribution network is a random optimization problem containing opportunity constraint as shown in formulas (8) to (17), and the opportunity constraint as shown in formula (16) describes the out-of-limit probability limit of the node voltage of the power distribution network, so that the actual operation requirement of the power distribution network containing the high-density distributed power supply is better met, and the feasibility of the power and reactive power combined scheduling scheme is ensured. The number of sample points required by the traditional Monte Carlo method is too large, the sample points exponentially rise along with the increase of the dimension, the calculation amount is very large, and dimension disasters can be met on the aspect of processing high-dimensional random parameters. Aiming at the defect, the deterministic convex equivalence model for the random optimization scheduling problem is provided based on a spectral decomposition approximation method.
S3: orthogonal polynomial approximation is carried out on a random space in the active and reactive power combined scheduling problem of the power distribution network based on a spectrum decomposition method, the random power flow space is sampled based on a sparse grid distribution point theory, a convex approximation certainty optimization model equivalent to a random optimization model is established,
the step S3 includes the following steps:
s3.1, expanding and approximating a random variable by using a chaotic polynomial (gPC), and then in the random economic dispatching model established in the step S2, obtaining the random variable
Figure GDA0003659270430000091
And
Figure GDA0003659270430000092
the K-th order gPC approximation polynomial is:
Figure GDA0003659270430000093
Figure GDA0003659270430000094
where K is the number of terms of the polynomial expansion, for the 5-dimensional random variable in this case
Figure GDA0003659270430000095
If the highest order of the polynomial is 3, the total number of terms K of the polynomial in the formula is 56;
Figure GDA0003659270430000096
is the basis function of the kth term of the orthogonal polynomial,
Figure GDA0003659270430000097
and
Figure GDA0003659270430000098
and the approximation coefficient corresponding to the k-th term base function. Different basis functions can be selected according to the distribution characteristics of random variables, as shown in table 1:
TABLE 1 optimal correspondences between orthogonal polynomials and random variables of various types
Type of random variable Orthogonal polynomial type Support set
Gussian Hermite (-∞，∞)
Gamma Laguerre [0，∞)
Beta Jacobi [a,b]
Uniform Legendre [a,b]
The orthogonal polynomial basis function satisfies the following orthogonal property,
Figure GDA0003659270430000099
in the formula, E2]The mathematical expectation is represented by the mathematical expectation,
Figure GDA00036592704300000910
is a basis function of the nth term of the orthogonal polynomial,
Figure GDA00036592704300000911
to a normalized constant, δ nk Is a Kronecker operator, and is a Kronecker operator,
Figure GDA00036592704300000912
as a random variable
Figure GDA00036592704300000913
Is determined. For the 5-dimensional random variables in this case
Figure GDA00036592704300000914
The basis functions in the polynomial expansions (10) to (11)
Figure GDA00036592704300000915
Is the tensor product of 5 univariate basis functions,
Figure GDA00036592704300000916
s3.2 establishing an opportunity-constrained deterministic convex approximation model based on a spectral method, for opportunity constraint
Figure GDA00036592704300000917
Available from the Cantelli's inequality, an equivalent of the following opportunistic constraints
Figure GDA00036592704300000918
As described in step 3.1, the random variable can be approximated by a K-th order gPC approximation polynomial which, based on the orthogonal nature of the orthogonal polynomial basis functions, knows,
Figure GDA0003659270430000101
Figure GDA0003659270430000102
substituting the inequality (22) above, a convex equivalent of the opportunity constraint (21) is obtained:
Figure GDA0003659270430000103
as can be seen, equation (26) relates to the gPC approximation coefficients
Figure GDA0003659270430000104
Is convex. The opportunity constraints (16) to (17) in the original active reactive power joint random optimization problem are equivalent to:
Figure GDA0003659270430000105
s3.3: s3.3: for N-5 dimensional random input variables
Figure GDA0003659270430000106
The sparse node sample set is constructed by utilizing Smolyak algorithm
Figure GDA0003659270430000107
And weight set of corresponding sparse node
Figure GDA0003659270430000108
In the present case, a 2-level Smolyak algorithm is adopted, the number M of sparse node samples is 50, a deterministic power flow equation is solved at each sample point to obtain a corresponding deterministic power flow equation,
Figure GDA0003659270430000109
Figure GDA00036592704300001010
Figure GDA00036592704300001011
by using the discrete Galerkin projection method based on sparse nodes, the coefficients of the Kth-order gPC expansions (18) and (19) are,
Figure GDA00036592704300001012
Figure GDA00036592704300001013
in the formula, σ m Representing sparse nodes
Figure GDA00036592704300001014
The corresponding weight.
In summary, the deterministic convex approximation optimization model of the random optimization scheduling can be obtained as shown in equations (8), (11) to (15), (18), (19) and (26) to (30). The number of samples obtained by the high-dimensional random space sparse nodes is much smaller than that of tensor product nodes, and the dimensionality disaster is relieved to a certain extent. In the scheme, the optimization tool box MOSEK is used for solving the established convex second-order cone optimization model to obtain a solution of active and reactive combined optimization scheduling of the power distribution network with the high-density distributed power supply. A sample set formed by sparse nodes is used for approaching to the optimal solution of the random space, so that the approaching precision of the understanding is ensured, and the dimension disaster of the active and reactive power combined optimization scheduling model of the power distribution network in the high-dimensional random parameter space is avoided.
The above-described embodiments are intended to illustrate rather than to limit the invention, and any modifications and variations of the present invention are within the spirit of the invention and the scope of the appended claims.

Claims (3)

1. A power distribution network optimal scheduling method considering random output of a high-density distributed power supply is characterized by comprising the following specific steps:
s1: establishing a low-order approximate model for simulating the random time sequence characteristics of the output of the distributed power supply by using a Karhunen-Loeve expansion representation method;
the random timing characteristic of the output of the analog distributed power supply comprises the following steps:
s1.1: due to the random fluctuation of the output of the wind power and the solar photovoltaic power supply, the injection power of the distributed power supply access node of the power distribution network at any moment t can be regarded as a random variable, and the random variable expands in a time dimension to form a random process; the injected power at distribution network node i at time t is described as:
Figure FDA0003659270420000011
Figure FDA0003659270420000012
in the formula (I), the compound is shown in the specification,
Figure FDA0003659270420000013
and
Figure FDA0003659270420000014
the active and reactive power output predicted values which are injected at the node i at the moment t are shown;
Figure FDA0003659270420000015
representing a node generator set, wherein WT is fan output of node injection, PV is photovoltaic output of node injection, and B is battery output of a node;
Figure FDA0003659270420000016
and
Figure FDA0003659270420000017
representing the active and reactive load predicted values at the node i at the time t;
Figure FDA0003659270420000018
representing a random variable;
Figure FDA0003659270420000019
and
Figure FDA00036592704200000110
the active and reactive prediction errors at a node i at the moment t are represented, and if the random characteristics of the errors at any moment t meet normal distribution, the prediction errors belong to a Gaussian random process;
s1.2: a Karhunen-Loeve expansion of the stochastic process was established and truncated by taking the top N terms as follows:
Figure FDA00036592704200000111
Figure FDA00036592704200000112
in the formula, N is the truncated order and xi n Are random variables that are not related to each other,
Figure FDA00036592704200000113
and
Figure FDA00036592704200000114
respectively random process correlation function C pp The characteristic value and the characteristic function of (c),
Figure FDA00036592704200000115
and
Figure FDA00036592704200000116
respectively random process correlation function C qq The characteristic value and the characteristic function satisfy:
Figure FDA00036592704200000117
Figure FDA00036592704200000118
where T is the grid operating period, T 1 And t 2 Respectively representing different time coordinates; the correlation function of the gaussian random process is sampled in exponential form:
Figure FDA0003659270420000021
in the formula I p And l q Respectively representing the correlation lengths of the active prediction error random process and the reactive prediction error random process;
s2: aiming at improving the quality of electric energy, establishing a power distribution network active and reactive power combined random optimization model containing power flow balance and opportunity constraint according to distributed power sources and load parameters, and concretely, the method comprises the following steps;
s2.1: the objective of the optimized dispatching is that the expected value of the active network loss in the power grid operation period T is minimum, namely
Figure FDA0003659270420000022
In the formula, E2]Represents a mathematical expectation;
Figure FDA0003659270420000023
Figure FDA0003659270420000024
an active network loss model on the power grid direct current tide; i denotes a node set of the distribution network, G ij Representing the real part of the ith row and j column elements of the nodal admittance matrix,
Figure FDA0003659270420000025
and
Figure FDA0003659270420000026
representing the node voltage amplitude of the power grid node i and the node j at the moment t;
s2.2: the method comprises the following steps of establishing a constraint condition of an active and reactive combined random optimization model of the power distribution network, and specifically comprising the following steps:
s2.2.1: stochastic power flow constraint
Figure FDA0003659270420000027
Figure FDA0003659270420000028
In the formula, G ij And B ij Respectively a real part and an imaginary part of j columns of elements in the ith row of the node admittance matrix;
Figure FDA0003659270420000029
and
Figure FDA00036592704200000210
respectively representing the amplitude and the phase angle of the j-th node voltage at the time t, wherein the node voltage and the amplitude are random variables due to the influence of random parameters of node injection power; random input parameters in tidal current constraints
Figure FDA00036592704200000211
And
Figure FDA00036592704200000212
as shown in formulas (3) to (4);
s2.2.2: battery charge and discharge power and capacity constraints
Figure FDA00036592704200000213
Figure FDA00036592704200000214
Figure FDA00036592704200000215
Figure FDA00036592704200000216
In the formula (I), the compound is shown in the specification,
Figure FDA00036592704200000217
representing the amount of stored energy of a battery installed at the i-node at time t, at representing the time span from t-1 to t, p b Which shows the charge-discharge efficiency of the battery,
Figure FDA00036592704200000218
and
Figure FDA00036592704200000219
respectively represent the lower limit and the upper limit of the charge-discharge power of a battery installed at the i-node, wherein
Figure FDA00036592704200000220
Which represents the maximum discharge power of the storage battery,
Figure FDA00036592704200000221
which indicates the maximum charging power of the storage battery,
Figure FDA00036592704200000222
and
Figure FDA00036592704200000223
respectively representing a lower limit and an upper limit of the amount of stored electricity of a battery installed at the i-node,
Figure FDA00036592704200000224
representing the reactive power supplied by the battery grid-connected converter at time t,
Figure FDA00036592704200000225
representing the capacity of the storage battery connected converter at the node i;
s2.2.3 distributed power supply active and reactive power output constraints
Figure FDA0003659270420000031
In the formula (I), the compound is shown in the specification,
Figure FDA0003659270420000032
and
Figure FDA0003659270420000033
respectively representing the upper limit of the active power output of the ith distributed power supply and the maximum capacity of the grid-connected converter;
s2.2.4: security opportunity constraints
Figure FDA0003659270420000034
Figure FDA0003659270420000035
In the formula, pr { } represents the probability of the inequality in braces being true;
Figure FDA0003659270420000036
and
Figure FDA0003659270420000037
respectively the allowable upper and lower limits of the voltage fluctuation at node i,
Figure FDA0003659270420000038
and
Figure FDA0003659270420000039
respectively represents the upper limit and the lower limit of the active power fluctuation of the branch transmission, 0.5<η<1 indicates that the opportunity constraint event is a large probability event;
s3: orthogonal polynomial approximation is carried out on a random space in the power distribution network active and reactive power combined random optimization problem based on a spectral decomposition method, the random power flow space is sampled based on a sparse grid distribution point theory, a convex approximation certainty optimization model equivalent to the random optimization model is established,
s3.1, expanding and approaching random power flow state variables by using a chaotic polynomial gPC (generalized stochastic programming model), and then in the random optimization scheduling model of the power distribution network active and reactive power combination established in the step S2, obtaining the random power flow state variables
Figure FDA00036592704200000310
And
Figure FDA00036592704200000311
the K-th order gPC approximation polynomial of (a) is described as:
Figure FDA00036592704200000312
Figure FDA00036592704200000313
in the formula, K is the number of terms of polynomial expansion,
Figure FDA00036592704200000314
is the basis function of the kth term of the orthogonal polynomial,
Figure FDA00036592704200000315
and
Figure FDA00036592704200000316
approximating coefficients corresponding to the k-th base function; the orthogonal polynomial basis function satisfies the following orthogonal property,
Figure FDA00036592704200000317
in the formula, E2]The mathematical expectation is represented by the mathematical expectation,
Figure FDA00036592704200000318
is a basis function of the nth term of the orthogonal polynomial,
Figure FDA00036592704200000319
to normalize constant, δ nk Is a Kronecker operator, and is a Kronecker operator,
Figure FDA00036592704200000320
as a random variable
Figure FDA00036592704200000321
A probability density function of;
s3.2 establishing an opportunity-constrained deterministic convex approximation model based on a spectral method, for opportunity constraint
Figure FDA00036592704200000322
Available from the Cantelli's inequality, an equivalent of the following opportunistic constraints
Figure FDA00036592704200000323
In the formula, Var [ ] represents the variance of a random variable;
according to S3.1, the random variable can be approximated by a Kth-order gPC approximation polynomial, and the mean value of the node voltage can be known according to the orthogonal property of the orthogonal polynomial basis function
Figure FDA0003659270420000041
Sum variance
Figure FDA0003659270420000042
Can be approximated by a polynomial coefficient,
Figure FDA0003659270420000043
Figure FDA0003659270420000044
substituting (23) and (24) into the above inequality (22) yields the convex equivalent of the opportunity constraint (21):
Figure FDA0003659270420000045
as can be seen, equation (25) relates to the gPC approximation coefficients
Figure FDA0003659270420000046
Convex constraint of (2); the opportunity constraints (16) to (17) in the original active reactive power joint random optimization problem are equivalent to:
Figure FDA0003659270420000047
s3.3: for N-dimensional random input variables
Figure FDA0003659270420000048
The sparse node sample set is constructed by utilizing Smolyak algorithm
Figure FDA0003659270420000049
And weight set of corresponding sparse node
Figure FDA00036592704200000410
Solving a deterministic power flow equation at each sample point to obtain a corresponding deterministic power flow equation,
Figure FDA00036592704200000411
Figure FDA00036592704200000412
Figure FDA00036592704200000413
solving the coefficients of the k-order gPC expansions (18) and (19) by using a discrete Galerkin projection method based on sparse nodes,
Figure FDA00036592704200000414
Figure FDA00036592704200000415
in the formula, σ m Representing sparse nodes
Figure FDA00036592704200000416
A corresponding weight;
the deterministic convex approximation optimization model of the random optimization scheduling of the power distribution network can be obtained and is shown in formulas (8), (11) to (15), (18), (19) and (26) to (30); and solving the convex optimization problem according to the deterministic convex approximation optimization model of the distribution network random optimization scheduling to obtain the distribution network optimization scheduling result.
2. The method according to claim 1, wherein in step S3.1, different basis functions are selected according to the distribution characteristics of the random variables.
3. The power distribution network optimal scheduling method considering the random output of the high-density distributed power supply as claimed in claim 1, wherein in step S3.3, the optimization tool box MOSEK, CVX is used to solve the convex optimization problem to obtain a solution containing the active and reactive power joint optimal scheduling of the high-density distributed power supply power distribution network.
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