CN111985720A - Second-order cone optimal power flow model based on distributed robustness and solving method - Google Patents

Second-order cone optimal power flow model based on distributed robustness and solving method Download PDF

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CN111985720A
CN111985720A CN202010879359.6A CN202010879359A CN111985720A CN 111985720 A CN111985720 A CN 111985720A CN 202010879359 A CN202010879359 A CN 202010879359A CN 111985720 A CN111985720 A CN 111985720A
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别朝红
肖遥
黄格超
高晓松
李更丰
贺元康
刘瑞丰
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Northwest Branch Of State Grid Power Grid Co
Xian Jiaotong University
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Abstract

The invention discloses a second-order cone optimal power flow model and a solving method based on distributed robustness, which comprises the following steps of: 1) decomposing a power flow equation into a linear part and a nonlinear part, and expressing the nonlinear part through auxiliary variables, wherein relaxation is second-order cone constraint, so that a second-order cone optimal power flow model is constructed, and simultaneously relaxation upper limit constraint is added to limit errors when a relaxation condition is not established; 2) according to the node power fluctuation, the prediction deviation of new energy and load is considered, Taylor expansion is carried out on the nonlinear part of the second-order cone optimal power flow model, a relation equation between uncertain quantities in the second-order cone optimal power flow model is deduced by combining the prediction deviation, expressions of the uncertain quantities are given at the same time, and a second-order cone optimization model for distributing the robust optimal power flow problem is established by combining an uncertain quantity chance constraint construction method and a variance interval estimation result.

Description

Second-order cone optimal power flow model based on distributed robustness and solving method
Technical Field
The invention belongs to the field of safety planning operation of an electric power system, and relates to a second-order cone optimal power flow model and a solving method based on distributed robustness.
Background
At present, the power grid dispatching or the electric power market clearing is calculated based on direct current load flow, reactive power and voltage cannot be effectively regulated, the result is lack of safety, and verification and adjustment are needed. And under the era background of global warming, environmental deterioration and energy crisis, the uncertainty of new energy power generation and load further increases the difficulty of safe operation of the power grid. In the united states, the Midwest mains network Operator (MISO) often intervenes in the load to meet voltage and reliability requirements.
An optimal power flow method capable of handling uncertainty and effectively controlling reactive power and voltage is urgently needed for an electric power system. A stable optimal tide solution taking uncertainty into account is the key to solving the above-mentioned problem.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a second-order cone optimal power flow model and a solving method based on distributed robustness.
In order to achieve the purpose, the second-order cone optimal power flow model and the solving method based on the distributed robustness comprise the following steps:
1) decomposing a power flow equation into a linear part and a nonlinear part, and expressing the nonlinear part through auxiliary variables, wherein relaxation is second-order cone constraint, so that a second-order cone optimal power flow model is constructed, and simultaneously relaxation upper limit constraint is added to limit errors when a relaxation condition is not established;
2) and the node power fluctuation considers the prediction deviation of new energy and load, Taylor expansion is carried out on the nonlinear part of the second-order cone optimal power flow model, a relational equation between uncertain quantities in the second-order cone optimal power flow model is deduced by combining the prediction deviation, expressions of the uncertain quantities are given at the same time, and a second-order cone optimization model for distributing the robust optimal power flow problem is established by combining an uncertain quantity opportunity constraint construction method and a variance interval estimation result.
The specific operation of decomposing the power flow equation into a linear part and a nonlinear part in the step 1) is as follows: dividing the power flow of the power transmission element into a lossless power flow and an impedance loss part, wherein the lossless power flow is used as a linear part, the impedance loss part is used as a nonlinear part, and the lossless power flow and the impedance loss part are respectively shown as a formula (3) and a formula (4):
Figure BDA0002653649530000021
Figure BDA0002653649530000022
wherein, ViAnd thetaiThe voltage amplitude and phase angle of the node i; gij、bijThe conductance and susceptance of the power transmission elements i-j.
The expression of the second-order cone constraint in the step 1) is as follows:
Figure BDA0002653649530000023
Figure BDA0002653649530000024
the second-order cone optimal power flow model constructed in the step 1) is as follows:
Figure BDA0002653649530000031
Figure BDA0002653649530000032
Figure BDA0002653649530000034
Figure BDA0002653649530000036
Figure BDA0002653649530000037
Figure BDA0002653649530000038
Figure BDA0002653649530000039
Figure BDA00026536495300000310
Figure BDA00026536495300000311
Figure BDA00026536495300000312
Figure BDA00026536495300000313
Figure BDA00026536495300000314
Figure BDA00026536495300000315
wherein, Pg、QgThe active and reactive outputs of the generator g are shown,
Figure BDA00026536495300000316
representing active and reactive loads of node i, Gij、BijRespectively the real part and the imaginary part, pi, of the row and the column elements of the admittance matrix iijFor the summation of the relaxation variables,
Figure BDA00026536495300000317
for generator-to-bus correlation matrix elements, when generator g is located at node i,
Figure BDA00026536495300000318
taking 1, otherwise, taking 0, N, Z as the maximum value of the serial numbers of the bus and the generator respectively, K is the set of the power transmission elements,
Figure BDA00026536495300000319
and
Figure BDA00026536495300000320
respectively representing the capacity parameters of the transmission element and the generator,
Figure BDA0002653649530000041
which represents the voltage limit of the node(s),
Figure BDA0002653649530000042
and lambdaijDual variables, gamma, for node power balance and power transmission element power respectivelyij、
Figure BDA0002653649530000043
The relevant dual variables representing the relaxation constraints,
Figure BDA0002653649530000044
a dual variable representing a grid safety constraint.
The expression of the error in step 1) is as follows:
Figure BDA0002653649530000045
in the step 2), the prediction deviation of the new energy and the load is as follows:
Figure BDA0002653649530000046
Figure BDA0002653649530000047
wherein the content of the first and second substances,
Figure BDA0002653649530000048
the predicted power of the bus i is represented,
Figure BDA0002653649530000049
and the active and reactive prediction errors are shown.
The uncertain quantity relation equation of the power system nodes in the step 2) is as follows:
EP P+VP V+TP θ＝0 (56)
EQ Q+VQ V+TQ θ＝0 (57)
the uncertain quantity relation equation of the line of the power system is as follows:
IJ+GIJ V+BIJ θ＝0 (58)
wherein G isIJ、BIJIn order to represent the line power error in a matrix,V、θthe coefficient matrix of (2).
The variance interval estimation result is:
the active and reactive power output safety constraints of the generator can be equivalent to:
Figure BDA00026536495300000410
Figure BDA00026536495300000411
Figure BDA0002653649530000051
Figure BDA0002653649530000052
the voltage safety constraints can be equated to:
Figure BDA0002653649530000053
Figure BDA0002653649530000054
the safety constraints on line power are:
Figure BDA0002653649530000055
Figure BDA0002653649530000056
the second-order cone optimization model of the distributed robust optimal power flow problem is as follows:
Figure BDA0002653649530000057
Figure BDA0002653649530000058
wherein (J)P)2、(JQ)2Representing the upper bound of the variance of active and reactive power of a node
Figure BDA0002653649530000059
Constituent column vectors, JP、JQRepresenting the upper bound of the active and reactive standard deviation of the node
Figure BDA00026536495300000510
A column vector of components.
The invention has the following beneficial effects:
the invention relates to a second-order cone optimal power flow model and a solving method based on distribution robustness, wherein during specific operation, node power fluctuation considers the prediction deviation of new energy and load, a relational equation between uncertain quantities in the second-order cone optimal power flow model is deduced by combining the prediction deviation, expressions of the uncertain quantities are given at the same time, a second-order cone optimal power flow model of the distribution robustness optimal power flow problem is established by combining an uncertain quantity chance constraint construction method and a variance interval estimation result, so as to ensure the safe operation of a power system, effectively cope with the uncertainty of the new energy and the load, and the invention aims at solving the problems that the traditional optimal power flow is not easy to popularize and the distribution robust method does not have calculation traceability in a power transmission network, the invention establishes the second-order cone optimal power flow model, further provides a distribution robust optimal model and a solution thereof, and is used in the power system, the operation cost of the system is reduced, and the safe operation of the power system can be guaranteed under the condition that the new energy and the load are uncertain.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of an example result of an IEEE57 node;
FIG. 3 is a graph of IEEE 1354 node generator output results;
FIG. 4 is a graph of IEEE 1354 node voltage and phase angle results;
FIG. 5 is a diagram of the apportionment of power fluctuations by the generator;
FIG. 6 is a voltage amplitude box plot for different safety probabilities;
fig. 7 is a line graph of the number of samples of violation constraints at different probabilities.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
the second-order cone optimal power flow model and the solving method based on the distributed robustness comprise the following steps:
1) decomposing a power flow equation into a linear part and a nonlinear part, and expressing the nonlinear part through auxiliary variables, wherein relaxation is second-order cone constraint, so as to construct a second-order cone optimal power flow model, and the error when a relaxation condition is not true is limited by increasing relaxation upper limit constraint;
2) and the node power fluctuation considers the prediction deviation of new energy and load, Taylor expansion is carried out on the nonlinear part of the second-order cone optimal power flow model, a relational equation between uncertain quantities in the second-order cone optimal power flow model is deduced by combining the prediction deviation, expressions of the uncertain quantities are given at the same time, and a second-order cone optimization model for distributing the robust optimal power flow problem is established by combining an uncertain quantity opportunity constraint construction method and variance interval estimation.
Specifically, the optimal power flow is abstractly expressed as shown in formulas (1) and (2), wherein formula (1) represents an optimization target, generally, the minimum fuel cost or the minimum active transmission loss of a unit is taken as the optimization target, the minimum active cost and the minimum reactive cost of the unit are taken as the optimization target, and formula (2) represents active power and reactive power balance constraint and safety constraint of a node.
Figure BDA0002653649530000071
Figure BDA0002653649530000072
P, Q respectively represents active and reactive output vectors of the generator; v and theta respectively represent the amplitude and phase angle vector of the node voltage; cP(·)、CQ(. is the active and reactive cost functions of the generator; f. ofP(·)、fQ(. g) and g (. cndot.) are power balance and safety constraint functions.
Dividing the power flow of the power transmission element into a lossless power flow and an impedance loss part, wherein the lossless power flow is shown as a formula (3) and a formula (4) respectively, and the lossless power flow is as follows: expressing the power flow of the line by the power flow of the midpoint of the power transmission line without recording the impedance loss of the line, and indicating that the admittance loss of the power transmission element to the ground is recorded as node loss and is positioned in a third part of the formula (14);
Figure BDA0002653649530000081
Figure BDA0002653649530000082
wherein, ViAnd thetaiThe voltage amplitude and phase angle of the node i; gij、bijThe conductance and susceptance of the power transmission elements i-j.
Due to the angular difference theta between two nodes of the transmission elementijLess than or equal to 30 degrees sin thetaijClose to 0, cos θijClose to 1, and hence simplified by equation (5).
Figure BDA0002653649530000083
Equations (3) and (4) are simplified into equations (6) and (7), and if the square of the node voltage amplitude and the phase angle are used as variables, equation (6) is a linear equation, so that only the nonlinear term in equation (7) needs to be processed.
Figure BDA0002653649530000084
Figure BDA0002653649530000085
Introducing auxiliary variables
Figure BDA0002653649530000086
And
Figure BDA0002653649530000087
respectively represent a nonlinear part-V in the formula (1)iVjAnd
Figure BDA0002653649530000088
as shown in the formulas (8) and (9), since the voltage is greater than 0, the voltage is set to be higher than 0
Figure BDA0002653649530000089
Equivalent formula (10).
Figure BDA00026536495300000810
Figure BDA00026536495300000811
Figure BDA00026536495300000812
Equations (10) and (9) are further relaxed into a second order cone constraint, which is expressed as:
Figure BDA0002653649530000091
Figure BDA0002653649530000092
in order to prevent the excessive error generated when the applicable condition of the relaxation is not established, the invention additionally supplements the constraint of the relaxation upper limit, as shown in formula (13), and the basic idea is as follows: at Vi∈[0.95,1.05]、θij∈[-30°,30°]Within the range of (a), find the distance-V from the relaxation object by linear fittingiVjAnd
Figure BDA0002653649530000093
the closest linear plane, while satisfying that the plane is larger than the object of the fit, then the relaxation variable is made
Figure BDA0002653649530000094
And
Figure BDA0002653649530000095
a linear plane smaller than the fitting object is the relaxation upper limit constraint, wherein,
Figure BDA0002653649530000096
the equation (13) is naturally satisfied, and can be omitted, and it is calculated that, -V is satisfied when the relaxation condition of a certain power transmission element is not satisfiediVjHas a maximum error of 0.005p.u.,
Figure BDA0002653649530000097
the maximum error of (2) is 0.137 rad.
Figure BDA0002653649530000098
The relation between the node injection power and the line power flow is shown as a formula (14), wherein the node injection power comprises lossless power flow and impedance loss of a power transmission element and earth loss.
Figure BDA0002653649530000099
Wherein the content of the first and second substances,
Figure BDA00026536495300000910
i-side to ground conduction and susceptance of the power transmission element ij, respectively.
Therefore, an optimal power flow model is obtained by combining the line power flow equations (6) and (7), the related constraints (11) to (13) of the second-order cone relaxation and the node injection power relational expression (14), as shown in the formulas (15) to (27), wherein the safety constraint considers the line capacity constraint, the node voltage constraint, the generator active power output constraint and the reactive power output constraint. Because the active loss of the line is low, the blocking degree of the line is generally measured by active power in a practical system, therefore, the invention expresses the capacity constraint (24) of the line by the lossless active power flow (23) of the line, and the invention expresses the variable quantity by the invention for convenience of expression
Figure BDA0002653649530000101
And
Figure BDA0002653649530000102
Figure BDA0002653649530000103
and the summation is expressed as shown in formula (18).
Figure BDA0002653649530000104
Figure BDA0002653649530000105
Figure BDA0002653649530000107
Figure BDA0002653649530000109
Figure BDA00026536495300001010
Figure BDA00026536495300001011
Figure BDA00026536495300001012
Figure BDA00026536495300001013
Figure BDA00026536495300001014
Figure BDA00026536495300001015
Figure BDA00026536495300001016
Figure BDA00026536495300001017
Figure BDA00026536495300001018
Wherein, Pg、QgThe active and reactive outputs of the generator g are shown,
Figure BDA00026536495300001019
representing active and reactive loads of node i, Gij、BijRespectively the real part and the imaginary part, pi, of the row and the column elements of the admittance matrix iijFor the summation of the relaxation variables,
Figure BDA00026536495300001020
for generator-to-bus correlation matrix elements, when generator g is located at node i,
Figure BDA00026536495300001021
taking 1, otherwise, taking 0, N, Z as the maximum value of the serial numbers of the bus and the generator respectively, K is the set of the power transmission elements,
Figure BDA0002653649530000111
and
Figure BDA0002653649530000112
respectively representing the capacity parameters of the transmission element and the generator,
Figure BDA0002653649530000113
which represents the voltage limit of the node(s),
Figure BDA0002653649530000114
and lambdaijDual variables, gamma, for node power balance and power transmission element power respectivelyij、
Figure BDA0002653649530000115
The relevant dual variables representing the relaxation constraints,
Figure BDA0002653649530000116
a dual variable representing a grid safety constraint.
In addition, the power error of the node comprises the prediction error of the load and the new energy, and the error causes the uncertainty of each state quantity in the power grid so as to
Figure BDA0002653649530000117
And m is an indeterminate quantity, the output power of the node is expressed as shown in a formula (34), wherein,
Figure BDA0002653649530000118
the predicted power of the bus i is represented,
Figure BDA0002653649530000119
Figure BDA00026536495300001110
Figure BDA00026536495300001111
representing active and reactive prediction errors, setting the prediction errors to be in accordance with normal distribution, and having no systematic defects, namely, the expectation is 0, and the variance is sigma2If the inter-prediction error correlation coefficient is 0, equation (35) is given, and the variance in equation (35) is an uncertainty.
Figure BDA00026536495300001112
Figure BDA00026536495300001113
According to the real-time control rule of the generators, in order to cope with power fluctuation in the system, the output of each generator is represented by the following formula (36) and formula (37), wherein alphagRepresenting the power fluctuation ratio, alpha, shared by the generator ggSatisfies the formula (38);
Figure BDA00026536495300001114
Figure BDA00026536495300001115
Figure BDA00026536495300001116
wherein the content of the first and second substances,P、Qto represent
Figure BDA00026536495300001117
Vector of composition, IP、IQIs the sum of all 1 row vectors and loss sensitivity row vectors, lossThe loss sensitivity vector represents the partial derivative of the network loss to the node power, either given empirically or by taking the difference quotient of the network loss to the node power based on the operating point.
Representing the rest variables of the network as the sum of the predicted quantity and the deviation, wherein the predicted quantity represents the value of the variable when the error is not predicted as shown in a formula (39);
Figure BDA0002653649530000121
the uncertain variables in the formula (34) -the formula (37) and the formula (39) are substituted into the node balance equations (16) and (17), and the uncertain variables are expressed in a matrix form as follows:
Figure BDA0002653649530000122
Figure BDA0002653649530000123
wherein, Vgen、VbranchRepresenting generator-bus, line-bus correlation matrix, AP、AQRepresenting diagonal line as alphagSquare matrix of LP、LQI indicating number of generatorsP、IQThe vector is connected in parallel to form a matrix, G, B is the real part and the imaginary part of the admittance array, wherein, diag (·) operation represents the matrix formed by setting the elements of the square matrix except the diagonal to zero,
Figure BDA0002653649530000126
coefficient matrix representing phase angle in active and reactive power balance, Gbranch、BbranchA diagonal matrix of elements in the admittance matrix for the power transmission element.
When no error exists, the predicted quantity naturally meets the equation of active and reactive power balance, so that the predicted quantity in the equations (40) and (41) is cancelled, and the relation between the uncertain quantities of the error is as follows:
Figure BDA0002653649530000124
Figure BDA0002653649530000125
since the predicted relaxation variables naturally satisfy the equations (44) and (45) and the error is not too large in consideration of uncertainty due to SOC relaxation and relaxation upper limit constraints, the relaxation variable expressions (8) and (9) containing random quantities can be subjected to taylor expansion, the expansion results are expressed by equations (46) and (47), and the error relationship of the relaxation variables is given by equation (18) and expressed by equation (48).
Figure BDA0002653649530000131
Figure BDA0002653649530000132
Figure BDA0002653649530000133
Figure BDA0002653649530000134
Figure BDA0002653649530000135
The relaxation error is obtained from the equation (44) -equation (47) and the error relationship (48) of the relaxation amount
Figure BDA0002653649530000136
Expression (49) of (1), wherein Vi、Vj、θi、θjGiven, relaxation error calculated from model under predicted conditions
Figure BDA0002653649530000137
The expression is shown in formula (50) in matrix form.
Figure BDA0002653649530000138
π＝HV+θ (50)
Wherein, H is a coefficient matrix of relaxation voltage error and is a coefficient matrix of relaxation phase angle error.
Bringing formula (50) into formulae (40) and (41) to obtainP、Q、V、θThe relation equation between the two is shown by combining the same terms as the formula (51) and the formula (52).
Figure BDA0002653649530000139
Figure BDA0002653649530000141
Wherein E represents a unit matrix.
The expressions (51) and (52) are simplified by the expressions (53), (54) and (55).
Figure BDA0002653649530000142
Figure BDA0002653649530000143
Figure BDA0002653649530000144
The electric power system node obtains an uncertain quantity relation equation as follows:
EP P+VP V+TP θ＝0 (56)
EQ Q+VQ V+TQ θ＝0 (57)
similarly, the line power equation (23) is rewritten into a matrix form, and the uncertainty relation equation of the line of the pre-measured power system is eliminated, which is shown in equation (58).
IJ+GIJ V+BIJ θ＝0 (58)
Wherein G isIJ、BIJIn order to represent the line power error in a matrix,V、θthe coefficient matrix of (2).
The model (DR-SOC-ACOPF) of the distributed robust optimal power flow is obtained as follows:
Figure BDA0002653649530000145
Figure BDA0002653649530000151
wherein the content of the first and second substances,
Figure BDA0002653649530000152
which represents the mathematical expectation operation,
Figure BDA0002653649530000153
representing probability operation, considering the safety constraint of uncertainty as the constraint of line, active power, reactive power and voltage being not less than 1-etaIJ、1-ηP、1-ηQ、1-ηVThe probability of (c) is satisfied.
Setting the cost function as a linear function, under the assumption that the mathematical expectation of the node prediction error is 0, the robust optimization target (59) can be equivalent to the formula (61);
Figure BDA0002653649530000154
when X follows a normal distributionN(μ,σ2) Constraint of probability
Figure BDA0002653649530000155
Is equivalent to formula (62), wherein, ζ1-ηRepresents the 1- η quantile of a standard normal distribution.
XMAX≥μ+ζ1-ησ (62)
Therefore, the safety constraints considering uncertainty are equivalent, and from equation (36) and equation (37), the generator active and reactive power output safety constraints can be equivalent to:
Figure BDA0002653649530000156
Figure BDA0002653649530000157
Figure BDA0002653649530000158
Figure BDA0002653649530000159
wherein (sigma)P)2、(σQ)2Respectively representing the active and reactive variances of the nodes
Figure BDA00026536495300001510
A column vector of composition, a, indicates a dot product operation of the matrix.
From equations (56) and (57), the error expression of the node voltage and the phase angle is obtained as:
V＝(TP(TQ)-1VQ-VP)-1EP P-(VQ-TQ(TP)-1VP)-1EQ Q (67)
θ＝(VP(VQ)-1TQ-TP)-1EP P-(TQ-VQ(VP)-1TP)-1EQ Q (68)
the voltage safety constraint can be equivalent to:
Figure BDA0002653649530000161
Figure BDA0002653649530000162
Figure BDA0002653649530000163
Figure BDA0002653649530000164
wherein [ ·]iThe ith row of the matrix is represented,
Figure BDA0002653649530000165
and
Figure BDA0002653649530000166
is the i row vector of the corresponding matrix.
The expressions (69) and (70) are expressed as second order tapered expressions, as shown in the expressions (73) and (74).
Figure BDA0002653649530000167
Figure BDA0002653649530000168
Similarly, the line power error can be expressed by the active and reactive errors as:
Figure BDA0002653649530000169
in the formula (75)PAndQis recorded as the ith row vector of the coefficient matrix
Figure BDA00026536495300001610
And
Figure BDA00026536495300001611
the safety constraint expression of the line power is obtained as shown in the formulas (76) and (77), and the second-order taper formulas are shown in the formulas (78) and (79).
Figure BDA00026536495300001612
Figure BDA0002653649530000171
Figure BDA0002653649530000172
Figure BDA0002653649530000173
By the expression, when the variance is fixed, the optimal power flow model is a second-order cone optimization problem and can be directly solved, and when the variance is an uncertain quantity, the worst variance value needs to be substituted to obtain the result of the complete distribution robust model.
The variance processing process comprises the following steps:
let historical node i error be
Figure BDA0002653649530000174
The true variance is (σ)i)2Estimate the variance of
Figure BDA0002653649530000175
Figure BDA0002653649530000176
Since the error follows a normal distribution that is expected to be 0, the estimate of the variance can be found from a minimum variance unbiased estimate, as shown in equation (80).
Figure BDA0002653649530000177
Since the number of history data satisfies T<Infinity, therefore variance estimation
Figure BDA00026536495300001713
Still has errors, and the normal distribution obeyed by the active errors of the same node is used for knowing
Figure BDA00026536495300001714
Obeying the chi-square distribution with the degree of freedom T, so as to calculate (sigma)i)2The value probability is not less than 1-etaσInterval of (1)
Figure BDA0002653649530000178
The upper and lower boundaries of the interval are shown in formula (81).
Figure BDA0002653649530000179
Wherein the content of the first and second substances,
Figure BDA00026536495300001710
is the 1- η quantile of the chi-square distribution with degree of freedom T.
Along with the increase of historical data, the value range of the variance is reduced, and the maximum value is taken in the variance under the condition of the worst uncertain safety constraint
Figure BDA00026536495300001711
The safety constraints are most difficult to satisfy. Finally obtaining a second-order conical mode of the DR-SOC-ACOPFThe type is as follows:
Figure BDA00026536495300001712
Figure BDA0002653649530000181
wherein (J)P)2、(JQ)2Representing the upper bound of the variance of active and reactive power of a node
Figure BDA0002653649530000182
Constituent column vectors, JP、JQRepresenting the upper bound of the active and reactive standard deviation of the node
Figure BDA0002653649530000183
A column vector of components.
The invention takes a plurality of IEEE examples as main examples for verifying the SOC-ACOPF, adjusts the IEEE57 node example and analyzes the calculation effect of the DR-SOC-ACOPF. The calculation result of the IEEE57 node is shown in FIG. 2, and the generator output calculated by the calculation of the IEEE 1354 node is shown in FIGS. 3 and 4, so that the method has better accuracy. In order to verify the invention, 23 nodes considering uncertainty are set in the calculation example, the uncertainty comprises active and reactive fluctuation, the mean value of the fluctuation is 0, the standard deviation is a load value which is 0.1 time, the loss sensitivity is 0.05, the number of samples is T900, the nodes are used as the basis of model solution, the proportion of the generator to the power fluctuation is calculated and obtained as shown in figure 5, the uncertainty of the power sharing of the machine components of No. 2, 4 and 6 with the output reaching the limit is avoided, and the proportion of the machine component of No. 5 with the lowest cost is maximized. Thus optimizing economy while ensuring safety. Fig. 6 is a box-type graph of voltage amplitude under different safety constraint probabilities, for describing the voltage quality, and it can be known that the higher the probability of safety requirement, the higher the voltage quality of the system. And 600 new random sample verification calculations were additionally generated. The ratio of the prediction quantity calculated by the model to the power fluctuation is shared, and simulation is performed by combining new random sample data, so that the number of samples violating the security constraint is calculated, as shown in fig. 7, as the probability of the security constraint increases, the probability of the variance interval increases, and the number of random samples violating the security constraint decreases. By setting a proper probability, the method can ensure the safety of the result, and the Gurobi solver under the MATLAB environment is adopted for solving the optimization problem.
The scope of the present invention is not limited to the above-described embodiments, and various modifications and variations of the present invention are intended to be included in the scope of the claims and their equivalents, which are described in the specification, for a person of ordinary skill in the art.

Claims (9)

1. A second-order cone optimal power flow model and a solving method based on distribution robustness are characterized by comprising the following steps:
1) decomposing a power flow equation into a linear part and a nonlinear part, and expressing the nonlinear part through auxiliary variables, wherein relaxation is second-order cone constraint, so that a second-order cone optimal power flow model is constructed, and simultaneously relaxation upper limit constraint is added to limit errors when a relaxation condition is not established;
2) and the node power fluctuation considers the prediction deviation of new energy and load, Taylor expansion is carried out on the nonlinear part of the second-order cone optimal power flow model, a relational equation between uncertain quantities in the second-order cone optimal power flow model is deduced by combining the prediction deviation, expressions of the uncertain quantities are given at the same time, and a second-order cone optimization model for distributing the robust optimal power flow problem is established by combining an uncertain quantity opportunity constraint construction method and a variance interval estimation result.
2. The distributed robust-based second-order cone optimal power flow model and solving method as claimed in claim 1, wherein the specific operation of decomposing the power flow equation into the linear part and the nonlinear part in step 1) is as follows: dividing the power flow of the power transmission element into a lossless power flow and an impedance loss part, wherein the lossless power flow is used as a linear part, the impedance loss part is used as a nonlinear part, and the lossless power flow and the impedance loss part are respectively shown as a formula (3) and a formula (4):
Figure FDA0002653649520000011
Figure FDA0002653649520000012
wherein, ViAnd thetaiThe voltage amplitude and phase angle of the node i; gij、bijThe conductance and susceptance of the power transmission elements i-j.
3. The distributed robust-based second-order cone optimal power flow model and solving method according to claim 1, wherein the expression of the second-order cone constraint in the step 1) is as follows:
Figure FDA0002653649520000021
Figure FDA0002653649520000022
4. the distributed robust-based second-order cone optimal power flow model and solving method according to claim 1, wherein the second-order cone optimal power flow model constructed in the step 1) is:
Figure FDA0002653649520000023
Figure FDA0002653649520000024
Figure FDA0002653649520000025
Figure FDA0002653649520000026
Figure FDA0002653649520000027
Figure FDA0002653649520000028
Figure FDA0002653649520000029
Figure FDA00026536495200000210
Figure FDA00026536495200000211
Figure FDA00026536495200000212
Figure FDA00026536495200000213
Figure FDA00026536495200000214
Figure FDA0002653649520000031
wherein, Pg、QgThe active and reactive outputs of the generator g are shown,
Figure FDA0002653649520000032
representing active and reactive loads of node i, Gij、BijRespectively the real part and the imaginary part, pi, of the row and the column elements of the admittance matrix iijFor the summation of the relaxation variables,
Figure FDA0002653649520000033
for generator-to-bus correlation matrix elements, when generator g is located at node i,
Figure FDA0002653649520000034
taking 1, otherwise, taking 0, N, Z as the maximum value of the serial numbers of the bus and the generator respectively, K is the set of the power transmission elements,
Figure FDA0002653649520000035
and
Figure FDA0002653649520000036
respectively representing the capacity parameters of the transmission element and the generator,
Figure FDA0002653649520000037
which represents the voltage limit of the node(s),
Figure FDA0002653649520000038
and lambdaijDual variables, gamma, for node power balance and power transmission element power respectivelyij、
Figure FDA0002653649520000039
The relevant dual variables representing the relaxation constraints,
Figure FDA00026536495200000310
a dual variable representing a grid safety constraint.
5. The distributed robust-based second-order cone optimal power flow model and solving method according to claim 1, wherein the expression of the error in the step 1) is as follows:
Figure FDA00026536495200000311
6. the distributed robust-based second-order cone optimal power flow model and solving method as claimed in claim 1, wherein in the step 2), the prediction deviation of the new energy and the load is as follows:
Figure FDA00026536495200000312
Figure FDA00026536495200000313
wherein the content of the first and second substances,
Figure FDA00026536495200000314
the predicted power of the bus i is represented,
Figure FDA00026536495200000315
and the active and reactive prediction errors are shown.
7. The distributed robust-based second-order cone optimal power flow model and solving method according to claim 1, wherein the uncertainty relation equation of the power system node in the step 2) is as follows:
EP P+VP V+TP θ＝0 (56)
EQ Q+VQ V+TQ θ＝0 (57)
the uncertain quantity relation equation of the line of the power system is as follows:
IJ+GIJ V+BIJ θ＝0 (58)
wherein G isIJ、BIJIn order to represent the line power error in a matrix,V、θthe coefficient matrix of (2).
8. The distributed robust-based second-order cone optimal power flow model and solving method as claimed in claim 1, wherein the variance interval estimation result is:
the active and reactive power output safety constraints of the generator can be equivalent to:
Figure FDA0002653649520000041
Figure FDA0002653649520000042
Figure FDA0002653649520000043
Figure FDA0002653649520000044
the voltage safety constraints can be equated to:
Figure FDA0002653649520000045
Figure FDA0002653649520000046
the safety constraints on line power are:
Figure FDA0002653649520000047
Figure FDA0002653649520000048
9. the distributed robust-based second-order cone optimal power flow model and solving method as claimed in claim 1, wherein the second-order cone optimal power flow model of the distributed robust optimal power flow problem is:
Figure FDA0002653649520000051
Figure FDA0002653649520000052
wherein (J)P)2、(JQ)2Representing the upper bound of the variance of active and reactive power of a node
Figure FDA0002653649520000053
Constituent column vectors, JP、JQRepresenting the upper bound of the active and reactive standard deviation of the node
Figure FDA0002653649520000054
A column vector of components.
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