CN111245012A - Link line power security domain characterization method considering new energy uncertainty - Google Patents

Link line power security domain characterization method considering new energy uncertainty Download PDF

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CN111245012A
CN111245012A CN202010093339.6A CN202010093339A CN111245012A CN 111245012 A CN111245012 A CN 111245012A CN 202010093339 A CN202010093339 A CN 202010093339A CN 111245012 A CN111245012 A CN 111245012A
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formula
new energy
uncertainty
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constraint
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杨知方
林伟
余娟
龙嘉锐
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Chongqing University
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Abstract

The invention discloses a method for representing a link line power security domain in consideration of new energy uncertainty, which mainly comprises a method for representing the link line power security domain in consideration of the new energy uncertainty based on a probability density function and a method for representing the link line power security domain in consideration of the new energy uncertainty based on interval number. The invention can fully consider the uncertainty of new energy and improve the representation precision of the combined line power security domain.

Description

Link line power security domain characterization method considering new energy uncertainty
Technical Field
The invention relates to the field of economic optimization calculation of an electric power system, in particular to a method for representing a tie line power security domain by considering uncertainty of new energy.
Background
The tie line power security domain is crucial to the safe consumption of new energy across regions. With large-scale new energy grid connection, the system uncertainty is increased sharply, so the new energy uncertainty needs to be considered in the representation of the power security domain of the tie line. However, the existing security domain characterization method can only perform characterization under the condition of fixed output of new energy (i.e. uncertainty of new energy cannot be considered). Meanwhile, although the uncertainty of new energy can be considered by using a probability density function or an upper and lower margin value of the power transmission capacity, the power transmission capacity still only provides the transmission capacity of a certain section at the boundary, and the transmission capacity of any power transmission combination at the boundary cannot be represented to completely evaluate the power transmission capacity of the system.
Disclosure of Invention
The present invention is directed to solving the problems of the prior art.
The technical scheme adopted for achieving the purpose of the invention is that the method for representing the power security domain of the tie line based on the probability density function and considering the uncertainty of the new energy mainly comprises the following steps:
1) establishing a constraint condition of the power safety of the tie line considering the uncertainty of new energy, and mainly comprising the following steps of:
1.1) establishing regional network power balance constraints, namely:
eGPG+eBPB+eRPR＝eDPD(1)
in the formula, PG、PB、PR、PDRepresenting generated electricity, tie line power, renewable power, and power demand, respectively. e.g. of the typeG、eB、eR、eDRespectively represent and PG、PB、PR、PDThe associated row vector.
1.2) establishing regional network generator capacity constraints, namely:
generated power PGShould not exceed the minimum outputP GAnd maximum output
Figure BDA0002384453470000011
Namely, it is
Figure BDA0002384453470000012
In the formula (I), the compound is shown in the specification,
Figure BDA0002384453470000013
()respectively represent upper and lower limits.
1.3) establishing regional network tie line power flow constraint, namely:
Figure BDA0002384453470000021
1.4) establishing the boundary phase angle limit of the regional network, namely:
eGPG+eDPD+eBPB＝0 (4)
1.5) establishing a regional network boundary phase angle thetaBThe relationship to power injection, namely:
θB＝XB×(MGPG+MBPB+MRPR+MDPD) (5)
in the formula, MG、MB、MR、MDRespectively represent and PG、PB、PR、PDThe associated incident matrix. XBIs the inverse of the susceptance matrix associated with the border node.
1.6) establishing regional network flow constraints, namely:
Figure BDA0002384453470000022
Pr(P f≤Pf)≥ε f (7)
wherein Pr (X. ltoreq. Y) ≥ Z is represented by the element XiNot more than element YiUnder the condition that the probability is not less than Zi. The subscript i denotes the number of elements in matrix X, matrix Y and matrix Z.
Figure BDA0002384453470000023
And ε f Representing the confidence probabilities associated with the upper and lower limits, respectively.
Pf＝S(MGPG+MBPB+MRPR+MDPD) (8)
Where S is a power transfer distribution matrix. PfIndicating branch traffic.
1.7) simplifying the formulas (1) to (8) to obtain the constraint condition of the power safety of the tie line considering the uncertainty of the new energy, namely:
h1PG+h2p+h3PR＝h4(9)
in the formula, the coupling variable of the connecting line
Figure BDA0002384453470000024
h1、h2、h3And h4Represents the constants calculated by the equations (1) and (5).
Pr(g1PG+g2p+b≤g3PR)≥ε (10)
In the formula, g1、g2、g3B and epsilon represent constants calculated by the equations (6) to (8).
Figure BDA0002384453470000025
Figure BDA0002384453470000026
In the formula (I), the compound is shown in the specification,pand
Figure BDA0002384453470000027
represents constants calculated by the formula (3) and the formula (4).
2) Converting the constraint condition of the tie line power safety considering the uncertainty of the new energy into a linear constraint condition of the tie line power safety considering the uncertainty of the new energy, and mainly comprising the following steps of:
2.1) converting the constraint condition of the tie line power safety considering the uncertainty of the new energy to obtain the opportunity constraint condition of the tie line power safety considering the uncertainty of the new energy, and the method mainly comprises the following steps:
2.1.1) noting that the number of border nodes is nBAnd set nBThe generator acts as a regulating generator. And converting the constraint condition (9) by using a Gaussian elimination method to obtain:
Figure BDA0002384453470000031
in the formula, matrix h1＝[h1Ah1F]。h1AAnd h1FThe sub-matrices relating to the regulated generator and the stationary generator are represented separately. The adjustable generator means that the output of the generator is adjustable, and the fixed generator means that the output of the generator is not adjustable. PGAIndicating regulating the power generation of the generator, PGFRepresenting the power generation of a stationary generator. H1H2, H3, and H4 denote parameter matrices.
2.1.2) converting the constraint (11) based on equation (13) to obtain:
Figure BDA0002384453470000032
2.1.3) converting the constraint (14) into an opportunistic constraint (15), namely:
Figure BDA0002384453470000033
2.1.4) converting the constraint (10) based on equation (13) to obtain an opportunity constraint (16), namely:
Pr(G1PGF+G2p+G4≤G3PR)≥ε (16)
in the formula, matrix G1＝g1F+g1AH1. Matrix g1＝[g1Ag1F]。g1AAnd g1FThe sub-matrices relating to the regulated generator and the stationary generator are represented separately. Matrix G2＝g1AH2+g2(ii) a Matrix G3＝g3-g1AH3. Matrix G4＝g1AH4+ b. ε is the probability threshold.
2.1.5) converting the constraint condition of the tie line power safety considering the uncertainty of the new energy based on the formulas (13) to (16) to obtain the opportunity constraint condition of the tie line power safety considering the uncertainty of the new energy, namely:
Figure BDA0002384453470000041
Figure BDA0002384453470000042
Pr(-F1PGF-F2p-F4≥-F3PR)≥εnew(19)
in the formula, F1、F2、F3The constant matrices calculated by the equations (15) and (16) are expressed. EpsilonnewRepresenting the confidence probabilities calculated by equation (15) and equation (16).
2.2) converting the opportunity constraint condition of the tie line power safety considering the uncertainty of the new energy to obtain the linear constraint condition of the tie line power safety considering the uncertainty of the new energy, and the main steps are as follows:
2.2.1) establishing an ith opportunity constraint expression in the opportunity constraint condition (19), namely:
Figure BDA0002384453470000043
in the formula, i represents the ith element of the matrix. The (i, #) denotes a matrix formed by the ith row of the matrix.
2.2.2) setting random variables
Figure BDA0002384453470000044
Based on cumulative distribution function
Figure BDA0002384453470000049
Converting the opportunistic constraint (20) into a linear constraint, namely:
Figure BDA0002384453470000045
in the formula, XηiIs the quantile.
2.2.3) computing cumulative distribution function using Cholesky decomposition strategy
Figure BDA00023844534700000410
The method mainly comprises the following steps:
2.2.3.1) will have correlation variables P of Pearson correlation matrix PRConversion to the variable γ, i.e.:
PR＝Gγ (22)
wherein ρ ═ GGT。
2.2.3.2) resets the random variable η, i.e.:
η＝-GF3γ＝Gηγ (23)
2.2.3.3) calculating the expected value μγAnd variance related to gamma
Figure BDA0002384453470000046
Namely:
μγ＝G-1μR(24)
Figure BDA0002384453470000047
in the formula, muRAnd
Figure BDA0002384453470000048
respectively, the expectation value and the variance of the normal distribution.
2.2.3.4) to establish an expected value μ for a random variable ηηSum variance
Figure BDA0002384453470000051
The expression, namely:
μη＝Gημγ(26)
Figure BDA0002384453470000052
2.2.3.5) will expect a value muRSum variance
Figure BDA0002384453470000053
Substituting into equations (26) and (27) yields:
μη＝GηG-1μR(28)
Figure BDA0002384453470000054
2.2.4) establish a linear constraint of the link power safety that takes into account the uncertainty of the new energy, i.e.
Figure BDA0002384453470000055
Figure BDA0002384453470000056
-F1PGF-F2p-F4≥Xη(32)
In the formula, XηFrom cumulative distribution density function
Figure BDA00023844534700000514
And quantile calculation. 1,2, …, nR。nRIs the number of new energy stations.
3) And determining a tie line power security domain which meets the linear constraint condition of the tie line power security considering the uncertainty of the new energy.
The method for representing the power security domain of the tie line based on the interval number and considering the uncertainty of new energy mainly comprises the following steps:
1) establishing regional network constraint conditions, namely:
Figure BDA0002384453470000057
Figure BDA0002384453470000058
Figure BDA0002384453470000059
Figure BDA00023844534700000510
in the formula, the new energy output lies in the interval
Figure BDA00023844534700000511
In (1). Lower limit of new energy output
Figure BDA00023844534700000512
Upper limit of new energy output
Figure BDA00023844534700000513
Figure BDA0002384453470000061
2) A joint linear programming model is established under all extreme renewable energy schemes, namely:
Figure BDA0002384453470000062
Figure BDA0002384453470000063
Figure BDA0002384453470000064
Figure BDA0002384453470000065
s∈K (41)
in the formula (I), the compound is shown in the specification,
Figure BDA0002384453470000066
and
Figure BDA0002384453470000067
is renewable energy and power generation in extreme cases s. K is the set of all extremes. The extreme case represents the output of the ith new energy station
Figure BDA0002384453470000068
Or
Figure BDA0002384453470000069
3) Simplifying equations (37) to (41) yields a joint linear simplified planning model under all extreme renewable energy scenarios, namely:
Figure BDA00023844534700000610
in the formula (I), the compound is shown in the specification,
Figure BDA00023844534700000611
indicating the amount of generated electricity
Figure BDA00023844534700000612
The vectors of the components.
Figure BDA00023844534700000613
Representing from renewable energy sources
Figure BDA00023844534700000614
The vectors of the components. F1、F2、F3And F4The constant matrix calculated from equation (37) to equation (41) is expressed.
4) Resolving a combined linear simplified programming model under all extreme renewable energy schemes to obtain a link line power security domain when the new energy is uncertain, and the method mainly comprises the following steps:
4.1) Link Power Security Domain when equation (42) is not empty
Figure BDA00023844534700000615
Variable of coupling of interconnection line
Figure BDA00023844534700000616
Q and W are parameter matrices.
4.2) when the formula (42) is empty, reconstructing the joint linear programming model according to different new energy extreme scenes, namely:
Figure BDA0002384453470000071
in the formula, | K | represents the number of new energy extreme scenarios.
Resolving the formula (43) to obtain a tie line power security domain
Figure BDA0002384453470000072
Figure BDA0002384453470000073
Is represented by the i-ththProjection of constraints (43) related to the new energy extreme scene scenario i into the space p.
It should be noted that, in consideration of two common characterization methods of the uncertainty of the new energy, the present invention correspondingly proposes two new methods to characterize the power security domain of the tie line in consideration of the uncertainty of the new energy. When the probability distribution function is used for describing the uncertainty of the new energy, the opportunity constraint is adopted to represent a tie line power security domain considering the uncertainty of the new energy, and then the opportunity constraint is converted into linear constraint based on quantile conversion of the cumulative distribution function. When describing the new uncertainty with the number of intervals, a joint linear programming model is proposed that considers all the extreme new energy scenarios.
The method has the advantages that the uncertainty of new energy can be fully considered, and the characterization precision of the combined linear power security domain is improved.
Drawings
FIG. 1 is a CDF curve;
FIG. 2 is a graph of the tie-line power security domain in space (P) when the probability density function is used to describe the new energy uncertaintyB5，PB9) Projection of (2);
FIG. 3 shows that the tie-line power security domain is in space (P) when the new energy uncertainty is described by the number of intervalsB5，PB9) Projection of (2);
FIG. 4 is a graph of the probability density function when describing the uncertainty of new energyThe tie-line power security domain is in space (P)B5，θB9) Projection of (2);
FIG. 5 shows that the tie-line power security domain is in space (P) when the new energy uncertainty is described by the number of intervalsB5，θB9) Projection of (2);
FIG. 6 is a graph of the tie-line power security domain in space (P) when the new energy uncertainty is described by a probability density functionB9，θB9) Projection of (2);
FIG. 7 shows that the tie-line power security domain is in space (P) when the new energy uncertainty is described by the number of intervalsB9，θB9) Is projected.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1, a method for characterizing a tie-line power security domain considering new energy uncertainty based on a probability density function mainly includes the following steps:
1) establishing a constraint condition of the power safety of the tie line considering the uncertainty of new energy, and mainly comprising the following steps of:
1.1) establishing regional network power balance constraints, namely:
eGPG+eBPB+eRPR＝eDPD(1)
in the formula, PG、PB、PR、PDRepresenting generated electricity, tie line power, renewable power, and power demand, respectively. e.g. of the typeG、eB、eR、eDRespectively represent and PG、PB、PR、PDThe associated row vector.
1.2) establishing regional network generator capacity constraints, namely:
generated power PGShould not exceed the minimum outputP GAnd maximum output
Figure BDA0002384453470000081
Namely, it is
Figure BDA0002384453470000082
In the formula (I), the compound is shown in the specification,
Figure BDA0002384453470000083
()respectively represent upper and lower limits.
1.3) establishing regional network tie line power flow constraint, namely:
Figure BDA0002384453470000084
in the formula (I), the compound is shown in the specification,
Figure BDA0002384453470000085
is the tie line maximum power.
1.4) the boundary phase angle should be between-pi and pi, i.e., the boundary phase angle of the area network is bounded as follows:
eGPG+eDPD+eBPB＝0 (4)
1.5) establishing a regional network boundary phase angle thetaBThe relationship to power injection, namely:
θB＝XB×(MGPG+MBPB+MRPR+MDPD) (5)
in the formula, MG、MB、MR、MDRespectively represent and PG、PB、PR、PDThe associated incident matrix. XBIs the inverse of the susceptance matrix associated with the border node.
1.6) establishing regional network flow constraints, namely:
Figure BDA0002384453470000091
Pr(P f≤Pf)≥ε f (7)
wherein Pr (X. ltoreq. Y) ≥ Z is represented by the element XiNot more than element YiUnder the condition that the probability is not less than Zi. The subscript i denotes the number of elements in matrix X, matrix Y and matrix Z.
Figure BDA0002384453470000092
And ε f Representing the confidence probabilities associated with the upper and lower limits, respectively.
Pf＝S(MGPG+MBPB+MRPR+MDPD) (8)
Where S is a power transfer distribution matrix. PfIndicating branch traffic.
1.7) simplifying the formulas (1) to (8) to obtain the constraint condition of the power safety of the tie line considering the uncertainty of the new energy, namely:
h1PG+h2p+h3PR＝h4(9)
in the formula, the coupling variable of the connecting line
Figure BDA0002384453470000093
h1、h2、h3And h4Represents the constants calculated by the equations (1) and (5).
Pr(g1PG+g2p+b≤g3PR)≥ε (10)
In the formula, g1、g2、g3B and epsilon represent constants calculated by the equations (6) to (8).
Figure BDA0002384453470000094
Figure BDA0002384453470000095
In the formula (I), the compound is shown in the specification,pand
Figure BDA0002384453470000096
represents constants calculated by the formula (3) and the formula (4).
2) Converting the constraint condition of the tie line power safety considering the uncertainty of the new energy into a linear constraint condition of the tie line power safety considering the uncertainty of the new energy, and mainly comprising the following steps of:
2.1) converting the constraint condition of the tie line power safety considering the uncertainty of the new energy to obtain the opportunity constraint condition of the tie line power safety considering the uncertainty of the new energy, and the method mainly comprises the following steps:
2.1.1) noting that the number of border nodes is nB. When considering the new energy uncertainty, n is set in order to keep (9) some generators should be allowed to adjust the contribution to eliminate the power imbalance caused by the new energy uncertaintyBThe generator acts as a regulating generator. And converting the constraint condition (9) by using a Gaussian elimination method to obtain:
Figure BDA0002384453470000101
in the formula, matrix h1＝[h1Ah1F]。h1AAnd h1FThe sub-matrices relating to the regulated generator and the stationary generator are represented separately. The adjustable generator means that the output of the generator is adjustable, and the fixed generator means that the output of the generator is not adjustable. PGAIndicating regulating the power generation of the generator, PGFRepresenting the power generation of a stationary generator; parameter matrix
Figure BDA0002384453470000102
Parameter matrix
Figure BDA0002384453470000103
Parameter matrix
Figure BDA0002384453470000104
And parameter matrix
Figure BDA0002384453470000105
2.1.2) converting the constraint (11) based on equation (13) to obtain:
Figure BDA0002384453470000106
2.1.3) converting the constraint (14) into an opportunistic constraint (15), namely:
Figure BDA0002384453470000107
2.1.4) converting the constraint (10) based on equation (13) to obtain an opportunity constraint (16), namely:
Pr(G1PGF+G2p+G4≤G3PR)≥ε (16)
in the formula, matrix G1＝g1F+g1AH1. Matrix g1＝[g1Ag1F]。g1AAnd g1FThe sub-matrices relating to the regulated generator and the stationary generator are represented separately. Matrix G2＝g1AH2+g2(ii) a Matrix G3＝g3-g1AH3. Matrix G4＝g1AH4+ b. ε is the probability threshold.
2.1.5) converting the constraint condition of the tie line power safety considering the uncertainty of the new energy based on the formulas (13) to (16) to obtain the opportunity constraint condition of the tie line power safety considering the uncertainty of the new energy, namely:
Figure BDA0002384453470000111
Figure BDA0002384453470000112
Pr(-F1PGF-F2p-F4≥-F3PR)≥εnew(19)
in the formula, F1、F2、F3The constant matrices calculated by the equations (15) and (16) are expressed. EpsilonnewRepresenting the confidence probabilities calculated by equation (15) and equation (16).
2.2) converting the opportunity constraint conditions of the tie line power safety considering the uncertainty of new energy, eliminating P from the opportunity constraint (19)RObtaining a linear constraint condition of the tie line power safety considering the uncertainty of the new energy, and mainly comprising the following steps of:
2.2.1) establishing an ith opportunity constraint expression in the opportunity constraint condition (19), namely:
Figure BDA0002384453470000113
in the formula, i represents the ith element of the matrix. The (i, #) denotes a matrix formed by the ith row of the matrix.
2.2.2) setting random variables
Figure BDA0002384453470000114
As shown in FIG. 1, when
Figure BDA0002384453470000115
Is greater than and
Figure BDA0002384453470000116
corresponding quantile XηiThen the opportunity constraint (20) may be satisfied. Thus, based on cumulative distribution functions
Figure BDA0002384453470000118
Converting the opportunistic constraint (20) into a linear constraint, namely:
Figure BDA0002384453470000117
in the formula, XηiIs the quantile.
2.2.3) computing cumulative distribution function using Cholesky decomposition strategy
Figure BDA0002384453470000119
The method mainly comprises the following steps:
2.2.3.1) will have correlation variables P of Pearson correlation matrix PRConversion to the variable γ, i.e.:
PR＝Gγ (22)
wherein ρ ═ GGT。
2.2.3.2) resets the random variable η, i.e.:
η＝-GF3γ＝Gηγ (23)
in the formula, matrix Gη＝-GF。
2.2.3.3) calculating the expected value μγAnd variance related to gamma
Figure BDA0002384453470000121
Namely:
μγ＝G-1μR(24)
Figure BDA0002384453470000122
in the formula, muRAnd
Figure BDA0002384453470000123
respectively, the expectation value and the variance of the normal distribution.
2.2.3.4) to establish an expected value μ for a random variable ηηSum variance
Figure BDA0002384453470000124
The expression, namely:
μη＝Gημγ(26)
Figure BDA0002384453470000125
2.2.3.5) will expect a value muRSum variance
Figure BDA0002384453470000126
Substituting into equations (26) and (27) yields:
μη＝GηG-1μR(28)
Figure BDA0002384453470000127
2.2.4) establish a linear constraint of the link power safety that takes into account the uncertainty of the new energy, i.e.
Figure BDA0002384453470000128
Figure BDA0002384453470000129
-F1PGF-F2p-F4≥Xη(32)
In the formula, XηFrom cumulative distribution density function
Figure BDA00023844534700001210
And quantile calculation. 1,2, …, nR。nRIs the number of new energy stations.
3) A Tie Line Power security domain meeting the linear constraint condition of Tie Line Power security considering the uncertainty of new energy is drawn for the Tie Line Power feasible domain by adopting the method in 'Z.Tan, H.ZHong, J.Wang, Q.Xia and C.Kang,' engineering Intra-Regional Constraints in Tie-Line Scheduling: A project-Based Framework ', IEEE trans.on Power Syst., vol.34, No.6, pp.4751-4761,2019'.
Example 2:
the method for representing the power security domain of the tie line based on the interval number and considering the uncertainty of new energy mainly comprises the following steps:
1) establishing regional network constraint conditions, namely:
Figure BDA0002384453470000131
Figure BDA0002384453470000132
Figure BDA0002384453470000133
Figure BDA0002384453470000134
in the formula, the new energy output lies in the interval
Figure BDA0002384453470000135
In (1). Lower limit of new energy output
Figure BDA0002384453470000136
Upper limit of new energy output
Figure BDA0002384453470000137
Figure BDA0002384453470000138
2) A joint linear programming model is established under all extreme renewable energy schemes, namely:
Figure BDA0002384453470000139
Figure BDA00023844534700001310
Figure BDA00023844534700001311
Figure BDA00023844534700001312
s∈K(41)
in the formula (I), the compound is shown in the specification,
Figure BDA00023844534700001313
and
Figure BDA00023844534700001314
is renewable energy and power generation in extreme cases s. K is the set of all extremes. The extreme case represents the output of the ith new energy station
Figure BDA00023844534700001315
Or
Figure BDA00023844534700001316
3) Simplifying equations (37) to (41) yields a joint linear simplified planning model under all extreme renewable energy scenarios, namely:
Figure BDA00023844534700001317
in the formula (I), the compound is shown in the specification,
Figure BDA00023844534700001318
indicating the amount of generated electricity
Figure BDA00023844534700001319
The vectors of the components.
Figure BDA00023844534700001320
Representing from renewable energy sources
Figure BDA00023844534700001321
The vectors of the components. F1、F2、F3And F4The constant matrix calculated from equation (37) to equation (41) is expressed.
4) Resolving a combined linear simplified programming model under all extreme renewable energy schemes to obtain a link line power security domain when the new energy is uncertain, and the method mainly comprises the following steps:
4.1) when the formula (42) is not empty, resolving to obtain a link Power security domain according to the prior method of ' Z.Tan, H.ZHong, J.Wang, Q.Xia and C.kang ', ' engineering Intra-Regional Constraints in Tie-Line Scheduling:, IEEE trans.on Power Syst., vol.34, No.6, pp.4751-4761,2019
Figure BDA0002384453470000141
Variable of coupling of interconnection line
Figure BDA0002384453470000142
Q and W are parameter matrices satisfying equation (42).
4.2) when the formula (42) is empty, reconstructing the joint linear programming model according to different new energy extreme scenes, namely:
Figure BDA0002384453470000143
in the formula, | K | represents the number of new energy extreme scenarios.
Resolving the formula (43) to obtain a tie line power security domain
Figure BDA0002384453470000144
Figure BDA0002384453470000145
Is represented by the i-ththProjection of constraints (43) related to the new energy extreme scene scenario i into the space p.
Example 2:
referring to fig. 2 to 7, an experiment for verifying the tie-line power security domain characterization method considering the new energy uncertainty disclosed in embodiment 1 and embodiment 2 mainly includes the following steps:
1) confirm the validity of the tie-line power security domain in fig. 2: a monte carlo simulation method is used. When describing reproducible uncertainty with a probability density function, 5000 random points within the feasible domain are generated
Figure BDA0002384453470000146
For each point, the feasibility of the opportunistic constraints (9) - (12) was examined by solving the following optimization problem:
Figure BDA0002384453470000151
simulation results show that all generated points can provide a solution (1) to the optimization problem. For the solutions, 5000 new energy scenes are further generated according to probability characteristics to check opportunity constraints, and confidence probability requirements can be met when the probability characteristics are found, so that the effectiveness of the method is proved.
2) Verifying the effectiveness of the described depicting method when the new energy is uncertain by adopting the interval number: generating 5000 random points in a tie-line power safety domain based on a Monte Carlo simulation method
Figure BDA0002384453470000152
And 5000 new energy scenarios were generated, demonstrating the feasibility of constraints (33) - (36) by solving the following optimization problem.
Figure BDA0002384453470000153
The numerical results show that all generation points can provide a solution to the optimization problem (2). Moreover, this demonstrates the effectiveness of our proposed method, given the obtained solution.

Claims (4)

1. The method for representing the power security domain of the tie line based on the probability density function and considering the uncertainty of the new energy is characterized by mainly comprising the following steps of:
1) and establishing a constraint condition of the power safety of the tie line considering the uncertainty of the new energy.
2) The constraint of the tie line power safety considering the uncertainty of the new energy is converted into a linear constraint of the tie line power safety considering the uncertainty of the new energy.
3) And determining a tie line power security domain which meets the linear constraint condition of the tie line power security considering the uncertainty of the new energy.
2. The method for characterizing the tie-line power security domain considering the uncertainty of the new energy based on the probability density function as claimed in claim 1 or 2, wherein the main steps of establishing the constraint condition of the tie-line power security considering the uncertainty of the new energy are as follows:
1) establishing a regional network power balance constraint, namely:
eGPG+eBPB+eRPR＝eDPD(1)
in the formula, PG、PB、PR、PDRepresenting generated energy, tie-line power, renewable power, and power demand, respectively; e.g. of the typeG、eB、eR、eDRespectively represent and PG、PB、PR、PDThe associated row vector;
2) establishing a regional network generator capacity constraint, namely:
generated power PGShould not exceed the minimum outputP GAnd maximum output
Figure FDA0002384453460000011
Namely, it is
Figure FDA0002384453460000012
In the formula (I), the compound is shown in the specification,
Figure FDA0002384453460000013
()respectively represent upper and lower limits;
3) establishing regional network tie line power flow constraint, namely:
Figure FDA0002384453460000014
4) establishing boundaries of boundary phase angles of the regional network, namely:
eGPG+eDPD+eBPB＝0 (4)
5) establishing a regional network boundary phase angle thetaBThe relationship to power injection, namely:
θB＝XB×(MGPG+MBPB+MRPR+MDPD) (5)
in the formula, MG、MB、MR、MDRespectively represent and PG、PB、PR、PDA correlated incidence matrix; xBIs the inverse of the susceptance matrix associated with the border node;
6) establishing regional network flow constraints, namely:
Figure FDA0002384453460000015
Pr(P f≤Pf)≥ε f (7)
wherein Pr (X. ltoreq. Y) ≥ Z is represented by the element XiNot more than element YiUnder the condition that the probability is not less than Zi(ii) a Subscript i represents the element number in matrix X, matrix Y and matrix Z;
Figure FDA0002384453460000021
and ε f Representing confidence probabilities associated with the upper and lower limits, respectively;
Pf＝S(MGPG+MBPB+MRPR+MDPD) (8)
wherein S is a power transfer distribution matrix; pfRepresenting branch flow;
7) simplifying the formula (1) to the formula (8) to obtain a constraint condition of the tie line power safety considering the uncertainty of the new energy, namely:
h1PG+h2p+h3PR＝h4(9)
in the formula, the connecting lines are coupledVariables of
Figure FDA0002384453460000022
h1、h2、h3And h4Constants obtained by calculation of the formula (1) and the formula (5) are expressed;
Pr(g1PG+g2p+b≤g3PR)≥ε (10)
in the formula, g1、g2、g3B and epsilon represent constants calculated by the formula (6) to the formula (8);
Figure FDA0002384453460000023
Figure FDA0002384453460000024
in the formula (I), the compound is shown in the specification,pand
Figure FDA0002384453460000025
represents constants calculated by the formula (3) and the formula (4).
3. The method for characterizing the tie-line power security domain considering the uncertainty of the new energy according to claim 1 or 2, wherein the main steps of converting the constraint condition of the tie-line power security considering the uncertainty of the new energy into a linear constraint condition are as follows:
1) converting the constraint condition of the tie line power safety considering the uncertainty of the new energy to obtain the opportunity constraint condition of the tie line power safety considering the uncertainty of the new energy, and the method mainly comprises the following steps:
1.1) noting the number of boundary nodes as nBAnd set nBThe generator is used as a regulating generator; and converting the constraint condition (9) by using a Gaussian elimination method to obtain:
Figure FDA0002384453460000031
in the formula, matrix h1＝[h1Ah1F]；h1AAnd h1FRepresenting the sub-matrices relating to the regulated generator and the stationary generator, respectively; the generator output is adjustable by adjusting the generator, and the generator output is not adjustable by fixing the generator; pGAIndicating regulating the power generation of the generator, PGFRepresenting the power generation of a stationary generator; h1H2, H3, and H4 denote parameter matrices;
1.2) converting the constraint (11) based on the formula (13) to obtain:
Figure FDA0002384453460000032
1.3) converting the constraint (14) into an opportunistic constraint (15), namely:
Figure FDA0002384453460000033
1.4) converting the constraint (10) based on equation (13) to obtain an opportunity constraint (16), namely:
Pr(G1PGF+G2p+G4≤G3PR)≥ε (16)
in the formula, matrix G1＝g1F+g1AH1(ii) a Matrix g1＝[g1Ag1F]；g1AAnd g1FRepresenting the sub-matrices relating to the regulated generator and the stationary generator, respectively; matrix G2＝g1AH2+g2；
Matrix G3＝g3-g1AH3(ii) a Matrix G4＝g1AH4+ b; epsilon is a probability threshold;
1.5) converting the constraint condition of the tie line power safety considering the uncertainty of the new energy based on the formulas (13) to (16) to obtain the opportunity constraint condition of the tie line power safety considering the uncertainty of the new energy, namely:
Figure FDA0002384453460000034
Figure FDA0002384453460000035
Pr(-F1PGF-F2p-F4≥-F3PR)≥εnew(19)
in the formula, F1、F2、F3Expressing the constant matrixes obtained by calculation of the formula (15) and the formula (16); epsilonnewRepresenting the confidence probabilities calculated by the formula (15) and the formula (16);
2) converting the opportunity constraint condition of the tie line power safety considering the uncertainty of the new energy to obtain the linear constraint condition of the tie line power safety considering the uncertainty of the new energy, and the method mainly comprises the following steps:
2.1) establishing an ith opportunity constraint expression in the opportunity constraint condition (19), namely:
Figure FDA0002384453460000041
wherein, i represents the ith element of the matrix; (i, #) denotes a matrix formed by the ith row of the matrix;
2.2) setting random variables
Figure FDA0002384453460000042
Based on cumulative distribution function CDF psiniThe opportunistic constraint (20) is converted into a linear constraint, namely:
Figure FDA0002384453460000043
in the formula, XηiIs quantile;
2.3) calculation of the cumulative distribution function CDF ψ using the Cholesky decomposition strategyniThe method mainly comprises the following steps:
2.3.1) correlating variables P with Pearson correlation matrix ρRConversion to the variable γ, i.e.:
PR＝Gγ (22)
wherein ρ ═ GGT；
2.3.2) reset the random variable η, i.e.:
η＝-GF3γ＝Gηγ (23)
2.3.3) calculating the expected value μγAnd variance related to gamma
Figure FDA0002384453460000044
Namely:
μγ＝G-1μR(24)
Figure FDA0002384453460000045
in the formula, muRAnd
Figure FDA0002384453460000046
respectively representing the expected value and the variance of normal distribution;
2.3.4) establishing the desired value μ of the random variable ηηSum variance
Figure FDA0002384453460000047
The expression, namely:
μη＝Gημγ(26)
Figure FDA0002384453460000048
2.3.5) will expect value μRSum variance
Figure FDA0002384453460000049
Substituting into equations (26) and (27) yields:
μη＝GηG-1μR(28)
Figure FDA0002384453460000051
2.4) establishing a linear constraint of the link power safety that takes into account the uncertainty of the new energy, i.e.
Figure FDA0002384453460000052
Figure FDA0002384453460000053
-F1PGF-F2p-F4≥Xη(32)
In the formula, XηFrom the cumulative distribution density function CDF psiniAnd calculating quantiles;
i＝1,2,…,nR；nRis the number of new energy stations.
4. The method for representing the power security domain of the tie line based on the interval number and considering the uncertainty of new energy is characterized by mainly comprising the following steps of:
1) establishing regional network constraint conditions, namely:
Figure FDA0002384453460000054
Figure FDA0002384453460000055
Figure FDA0002384453460000056
Figure FDA0002384453460000057
in the formula, the new energy output lies in the interval
Figure FDA0002384453460000058
Performing the following steps; lower limit of new energy output
Figure FDA0002384453460000059
Upper limit of new energy output
Figure FDA00023844534600000510
Figure FDA00023844534600000511
i＝1,2,…,nR；
2) A joint linear programming model is established under all extreme renewable energy schemes, namely:
Figure FDA00023844534600000512
Figure FDA00023844534600000513
Figure FDA00023844534600000514
Figure FDA00023844534600000515
s∈K (41)
in the formula (I), the compound is shown in the specification,
Figure FDA0002384453460000061
and
Figure FDA0002384453460000062
is renewable energy and generating capacity under an extreme condition s; k is the set of all extremes; the extreme case represents the output of the ith new energy station
Figure FDA0002384453460000063
Or
Figure FDA0002384453460000064
3) Simplifying equations (37) to (41) yields a joint linear simplified planning model under all extreme renewable energy scenarios, namely:
Figure FDA0002384453460000065
in the formula (I), the compound is shown in the specification,
Figure FDA0002384453460000066
indicating the amount of generated electricity
Figure FDA0002384453460000067
A vector of components;
Figure FDA0002384453460000068
representing from renewable energy sources
Figure FDA0002384453460000069
A vector of components; f1、F2、F3And F4Represents a constant matrix calculated from formula (37) to formula (41);
4) resolving a combined linear simplified programming model under all extreme renewable energy schemes to obtain a link line power security domain when the new energy is uncertain, and the method mainly comprises the following steps:
4.1) Link Power Security Domain when equation (42) is not empty
Figure FDA00023844534600000610
Variable of coupling of interconnection line
Figure FDA00023844534600000611
Q and W are parameter matrixes;
4.2) when the formula (42) is empty, reconstructing the joint linear programming model according to different new energy extreme scenes, namely:
Figure FDA00023844534600000612
in the formula, | K | represents the number of the new energy extreme scenes;
resolving the formula (43) to obtain a tie line power security domain
Figure FDA00023844534600000613
Figure FDA00023844534600000614
Is represented by the i-ththProjection of constraints (43) related to the new energy extreme scene scenario i into the space p.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112434402A (en) * 2020-10-22 2021-03-02 天津大学 Interval practical safety domain modeling method
CN113486509A (en) * 2021-07-01 2021-10-08 天津大学 Multi-objective optimization control method for comprehensive energy system

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112434402A (en) * 2020-10-22 2021-03-02 天津大学 Interval practical safety domain modeling method
CN113486509A (en) * 2021-07-01 2021-10-08 天津大学 Multi-objective optimization control method for comprehensive energy system
CN113486509B (en) * 2021-07-01 2023-02-28 天津大学 Multi-objective optimization control method for comprehensive energy system

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