CN111985720B - Second order cone optimal power flow model and solving method based on distribution robustness - Google Patents
Second order cone optimal power flow model and solving method based on distribution robustness Download PDFInfo
- Publication number
- CN111985720B CN111985720B CN202010879359.6A CN202010879359A CN111985720B CN 111985720 B CN111985720 B CN 111985720B CN 202010879359 A CN202010879359 A CN 202010879359A CN 111985720 B CN111985720 B CN 111985720B
- Authority
- CN
- China
- Prior art keywords
- power flow
- order cone
- optimal power
- constraint
- flow model
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 17
- 230000014509 gene expression Effects 0.000 claims abstract description 27
- 238000010276 construction Methods 0.000 claims abstract description 5
- 230000005540 biological transmission Effects 0.000 claims description 22
- 239000013598 vector Substances 0.000 claims description 15
- 239000011159 matrix material Substances 0.000 description 23
- 230000009977 dual effect Effects 0.000 description 6
- 238000005457 optimization Methods 0.000 description 6
- 238000004364 calculation method Methods 0.000 description 3
- 238000002347 injection Methods 0.000 description 3
- 239000007924 injection Substances 0.000 description 3
- 239000000243 solution Substances 0.000 description 3
- 230000007547 defect Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000035945 sensitivity Effects 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 235000015429 Mirabilis expansa Nutrition 0.000 description 1
- 244000294411 Mirabilis expansa Species 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000000903 blocking effect Effects 0.000 description 1
- 230000001276 controlling effect Effects 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 230000006866 deterioration Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000007613 environmental effect Effects 0.000 description 1
- 239000000446 fuel Substances 0.000 description 1
- 238000012886 linear function Methods 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 235000013536 miso Nutrition 0.000 description 1
- 238000012821 model calculation Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000010248 power generation Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 230000001681 protective effect Effects 0.000 description 1
- 230000001105 regulatory effect Effects 0.000 description 1
- 239000013589 supplement Substances 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
- 238000012795 verification Methods 0.000 description 1
- 238000010792 warming Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
- G06Q50/06—Energy or water supply
Landscapes
- Business, Economics & Management (AREA)
- Engineering & Computer Science (AREA)
- Economics (AREA)
- Human Resources & Organizations (AREA)
- Strategic Management (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- Marketing (AREA)
- General Physics & Mathematics (AREA)
- General Business, Economics & Management (AREA)
- Tourism & Hospitality (AREA)
- Quality & Reliability (AREA)
- Game Theory and Decision Science (AREA)
- Operations Research (AREA)
- Development Economics (AREA)
- Entrepreneurship & Innovation (AREA)
- Public Health (AREA)
- Water Supply & Treatment (AREA)
- General Health & Medical Sciences (AREA)
- Primary Health Care (AREA)
- Supply And Distribution Of Alternating Current (AREA)
Abstract
The invention discloses a second order cone optimal power flow model and a solving method based on distribution robustness, which comprises the following steps: 1) Decomposing a power flow equation into a linear part and a nonlinear part, and expressing the nonlinear part through an auxiliary variable, wherein relaxation is a second-order cone constraint, so as to construct a second-order cone optimal power flow model, and meanwhile, adding a relaxation upper limit constraint to limit errors when a relaxation condition is not established; 2) The node power fluctuation considers the prediction deviation of new energy and load, the nonlinear part of the second order cone optimal power flow model is subjected to Taylor expansion, the relation equation between uncertain quantities in the second order cone optimal power flow model is deduced by combining the prediction deviation, meanwhile, expressions of the uncertain quantities are given, and a second order cone optimal 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.
Description
Technical Field
The invention belongs to the field of safety planning operation of power systems, and relates to a second order cone optimal power flow model and a solving method based on distribution robustness.
Background
At present, power grid dispatching or power market clearing is calculated based on direct current power flow, reactive power and voltage cannot be effectively regulated and controlled, and the result lacks safety and needs checksum adjustment. In the age 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 midwestern grid operators (MIDWEST INDEPENDENT SYSTEM operators, MISOs) often intervene on the load to meet voltage and reliability requirements.
The power system is in urgent need of an optimal power flow method capable of handling uncertainty and effectively controlling reactive power and voltage. A stable optimal power flow solution taking uncertainty into account is a key to solving the above-mentioned problems.
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 distribution robustness.
In order to achieve the above purpose, the second order cone optimal power flow model and solving method based on the distribution robustness of the invention comprises the following steps:
1) Decomposing a power flow equation into a linear part and a nonlinear part, and expressing the nonlinear part through an auxiliary variable, wherein relaxation is a second-order cone constraint, so as to construct a second-order cone optimal power flow model, and meanwhile, adding a relaxation upper limit constraint to limit errors when a relaxation condition is not established;
2) The node power fluctuation considers the prediction deviation of new energy and load, the nonlinear part of the second order cone optimal power flow model is subjected to Taylor expansion, the relation equation between uncertain quantities in the second order cone optimal power flow model is deduced by combining the prediction deviation, meanwhile, expressions of the uncertain quantities are given, and the second order cone optimal model for distributing the robust optimal power flow problem is established by combining the uncertain quantity opportunity constraint construction method and the variance interval estimation result.
The specific operation of decomposing the tide equation into the linear part and the 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 taken as a linear part, the impedance loss part is taken 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):
Wherein V i and θ i are the voltage amplitude and phase angle of node i; g ij、bij is the conductance and susceptance of the power transmission element i-j.
The expression of the second order cone constraint in step 1) is:
the second order cone optimal power flow model constructed in the step 1) is as follows:
Wherein P g、Qg represents the active and reactive output of the generator g, Representing the active and reactive loads of node i, G ij、Bij being the real and imaginary parts of the elements of row j and column i of the admittance matrix, respectively, pi ij being the summation of the relaxation variables,/>As the associated matrix element of the generator and the bus, when the generator g is positioned at the node i,/>Taking 1, otherwise taking 0, N and Z as the maximum values of the serial numbers of the bus and the generator respectively, K as the collection of power transmission elements,/>/>Representing the capacity parameters of the power transmission element and the generator, respectively,/>Representing the voltage limit of the node,/>And lambda ij are the dual variables of node power balance and active power of the power transmission element, gamma ij,/>, respectivelyThe relevant dual variables representing the relaxation constraint,A dual variable representing a grid safety constraint.
The expression of the error in step 1) is:
In the step 2), the prediction deviation of the new energy and the load is as follows:
Wherein, Representing predicted power of bus i,/>Representing the active and reactive prediction errors.
The relation equation of the uncertainty of the power system node in the step 2) is as follows:
EPεP+VPεV+TPεθ＝0 (56)
EQεQ+VQεV+TQεθ＝0 (57)
the uncertainty relation equation of the line of the power system is:
εIJ+GIJεV+BIJεθ＝0 (58)
where G IJ、BIJ is a coefficient matrix of ε V、εθ when the line power error is represented by a matrix.
The variance interval estimation result is:
the active and reactive output safety constraint of the generator can be equivalently:
the voltage safety constraint may be equivalently:
The safety constraints of line power are:
The second order cone optimization model for distributing the robust optimal power flow problem is as follows:
Wherein (J P)2、(JQ)2) represents the upper bound of the active and reactive variances of the nodes The column vector, J P、JQ, represents the node active and reactive standard deviation upper bound/>A column vector of components.
The invention has the following beneficial effects:
When the distributed robust-based second-order cone optimal power flow model and the solving method are specifically operated, the node power fluctuation considers the prediction deviation of new energy and load, the relation equation between uncertain quantities in the second-order cone optimal power flow model is deduced by combining the prediction deviation, expressions of all uncertain quantities are given out, and a second-order cone optimal model of the distributed robust optimal power flow problem is established by combining an uncertain quantity opportunity constraint construction method and a variance interval estimation result, so that safe operation of a power system is ensured, the uncertainty of the new energy and the load is effectively solved, and the problem that the traditional optimal power flow solution is not suitable for popularization and the distributed robust method does not have calculation traceability in a power transmission network is solved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is an IEEE 57 node calculation example result diagram;
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 plot of generator versus power fluctuation split ratio;
FIG. 6 is a box plot of voltage amplitude for different safety probabilities;
FIG. 7 is a plot of the number of samples of violation constraint at different probabilities.
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures:
The second order cone optimal power flow model and solving method based on the distribution 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 an auxiliary variable, wherein the relaxation is a second order cone constraint, so as to construct a second order cone optimal power flow model, and limiting the error when a relaxation condition is not established by adding a relaxation upper limit constraint;
2) The node power fluctuation considers the prediction deviation of new energy and load, the nonlinear part of the second order cone optimal power flow model is subjected to Taylor expansion, the relation equation between uncertain quantities in the second order cone optimal power flow model is deduced by combining the prediction deviation, meanwhile, expressions of the uncertain quantities are given, and the second order cone optimal model for distributing the robust optimal power flow problem is established by combining the uncertain quantity opportunity constraint construction method and variance interval estimation.
Specifically, the optimal power flow abstract expression is shown in formulas (1) and (2), wherein (1) represents an optimization target, and the optimization target is generally the minimum fuel cost or minimum active transmission loss of a unit.
Wherein P, Q respectively represent the active and reactive output vectors of the generator; v and theta respectively represent the amplitude and phase angle vectors of the node voltage; c P(·)、CQ (·) is the active and reactive cost function of the generator; f P(·)、fQ (·) and g (·) are power balancing and security constraint functions.
Dividing the power flow of the power transmission element into a lossless power flow and an impedance loss part, as shown in a formula (3) and a formula (4), respectively, wherein 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, wherein the admittance loss of the power transmission element to the ground is recorded as node loss and is positioned in the third part of the formula (14);
Wherein V i and θ i are the voltage amplitude and phase angle of node i; g ij、bij is the conductance and susceptance of the power transmission element i-j.
Since the difference θ ij between the two nodes of the power transmission element is 30 ° or less, sin θ ij is close to 0, and cos θ ij is close to 1, the simplification is performed by the equation (5).
The equations (3) and (4) are simplified to the equations (6) and (7), and if the square and phase angle of the node voltage amplitude are used as variables, the equation (6) is a linear equation, so that only the nonlinear term in the equation (7) needs to be processed.
Introducing auxiliary variables/>Respectively represent the nonlinear part-V iVj and/>, in the formula (1)As shown in the formulas (8) and (9), the voltage is greater than 0, so/>Can be equivalently represented by formula (10).
Equation (10) and equation (9) are further relaxed to a second order cone constraint, the expression of which is:
In order to prevent excessive error when the applicable condition of relaxation is not satisfied, the invention additionally supplements the upper limit constraint of relaxation, as shown in a formula (13), and the basic idea is as follows: finding the distance loose object-V iVj and the distance loose object-V iVj by linear fitting within the range of V i∈[0.95,1.05]、θij epsilon [ -30 DEG, 30 DEG ] The closest linear plane, while satisfying that the plane is larger than the fitting object, then let the relaxation variable/>And/>A linear plane smaller than the fitting object is a relaxation upper limit constraint, wherein,/>The expression (13) is naturally true, and can be omitted, and when the relaxation condition of a certain power transmission element is not true, the maximum error of-V iVj is 0.005p.u.,The maximum error of (2) is 0.137rad.
The relation between the node injection power and the line power flow is shown in the formula (14), wherein the node injection power comprises lossless power flow, impedance loss and ground loss of the power transmission element.
Wherein,The i-side pair of the power transmission element ij is grounded and the pair of the power transmission element ij is grounded.
Therefore, by combining the line power flow equations (6) and (7), the related constraints (11) - (13) of second order cone relaxation and the node injection power relation (14), an optimal power flow model is obtained, as shown in the formulas (15) to (27), wherein the safety constraint considers the line capacity constraint, the node voltage constraint, the generator active output and the reactive output constraint. Because the active loss of the line is low, the active power is also commonly used for measuring the blocking degree of the line in an actual system, and therefore, the invention expresses the capacity constraint (24) of the line by using the lossless active power flow (23) of the line, and the invention uses the variable for the convenience of expressionAnd/> The sum is represented by equation (18).
Wherein P g、Qg represents the active and reactive output of the generator g,Representing the active and reactive loads of node i, G ij、Bij being the real and imaginary parts of the elements of row j and column i of the admittance matrix, respectively, pi ij being the summation of the relaxation variables,/>As the associated matrix element of the generator and the bus, when the generator g is positioned at the node i,/>Taking 1, otherwise taking 0, N and Z as the maximum values of the serial numbers of the bus and the generator respectively, K as the collection of power transmission elements,/>/>Representing the capacity parameters of the power transmission element and the generator, respectively,/>Representing the voltage limit of the node,/>And lambda ij are the dual variables of node power balance and active power of the power transmission element, gamma ij,/>, respectivelyThe relevant dual variables representing the relaxation constraint,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 uncertainty of each state quantity in the power grid so as toAnd m is an uncertainty amount, the output power of the node is represented by equation (34), wherein,Representing predicted power of bus i,/> The prediction error epsilon is set to be compliant with normal distribution, and no systematic defect is caused, namely, the expected value is 0, the variance is sigma 2, and the correlation coefficient between the prediction errors is 0, and the prediction error epsilon is set to be in a formula (35), wherein the variance is an uncertainty in the formula (35).
According to a real-time control rule of the generators, in order to cope with power fluctuation in a system, the output of each generator is shown as a formula (36) and a formula (37), wherein alpha g represents the power fluctuation proportion of the generator g, and alpha g meets a formula (38);
Wherein ε P、εQ represents The component vector, I P、IQ, is the sum of the full 1-row vector and the loss sensitivity row vector, which represents the partial derivative of the network loss to the node power, given empirically, or obtained by taking the difference quotient of the network loss to the node power based on the operating point.
The rest variables of the network are expressed as the sum of the predicted quantity and the deviation, and the predicted quantity represents the value of the predicted error-free time variable as shown in a formula (39);
the uncertainty variables in the formulas (34) - (37) and (39) are brought into the node balance equations (16) and (17), and are expressed as a matrix:
Wherein V gen、Vbranch represents a generator-bus and line-bus incidence matrix, A P、AQ represents a square matrix with a diagonal of alpha g, L P、LQ represents a matrix formed by parallel connection of I P、IQ vectors of the number of generators, G, B is a real part and an imaginary part of an admittance matrix, wherein diag (&) operation represents a matrix formed by zeroing elements of the square matrix except for the diagonal, And G branch、Bbranch is a diagonal matrix formed by elements of the power transmission element in the admittance matrix.
When there is no error, the predicted quantity naturally satisfies the active and reactive balance equations, so that the predicted quantity in the formulas (40) and (41) is canceled, and the relation between the uncertainty quantities of the error is obtained as follows:
From the SOC relaxation and the relaxation upper limit constraint, it is considered that the predicted relaxation variable naturally satisfies the expression (44) and the expression (45), and the error is not too large when the uncertainty is considered, so that the relaxation variable expressions (8) and (9) containing random amounts can be taylor-expanded, the expansion result is shown as the expression (46) and the expression (47), and the error relation of the relaxation variable is given by the expression (18), as shown as the expression (48).
Obtaining a relaxation error from the error relation (48) between the formulas (44) to (47) and the relaxation amountWherein V i、Vj、θi、θj is given by model calculation under predictive conditions, relaxation error/>The expression is shown in a matrix form as shown in a formula (50).
επ＝HεV+Γεθ (50)
Where H is the coefficient matrix of the relaxation voltage error and Γ is the coefficient matrix of the relaxation phase angle error.
And (3) taking the formula (50) into the formula (40) and the formula (41) to obtain a relational equation between epsilon P、εQ、εV、εθ, and combining the similar terms as shown in the formula (51) and the formula (52).
Wherein E represents a unit array.
The expression (51) and the expression (52) are simplified by using the expression (53), the expression (54) and the expression (55).
The power system node obtains an uncertainty relation equation as follows:
EPεP+VPεV+TPεθ＝0 (56)
EQεQ+VQεV+TQεθ＝0 (57)
similarly, the line power equation (23) is rewritten into a matrix form, and the predetermined amount is eliminated, and the uncertainty amount relation equation of the line of the electric power system is obtained, as shown in the formula (58).
εIJ+GIJεV+BIJεθ＝0 (58)
Where G IJ、BIJ is a coefficient matrix of ε V、εθ when the line power error is represented by a matrix.
The model (DR-SOC-ACOPF) for distributing the robust optimal power flow is:
Wherein, Representing mathematical expectation operations,/>The probability operation is represented, and the safety constraint taking uncertainty into consideration is that the probability that the constraint of the line, the active power, the reactive power and the voltage is not smaller than 1-eta IJ、1-ηP、1-ηQ、1-ηV is satisfied.
Setting the cost function as a linear function, the robust optimization objective (59) can be equivalently expressed as a formula (61) under the assumption that the mathematical expectation of the node prediction error is 0;
When X obeys normal distribution N (mu, sigma 2), probability constraint The equivalent is formula (62), wherein ζ 1-η represents the 1- η quantile of the standard normal distribution.
XMAX≥μ+ζ1-ησ (62)
Therefore, the safety constraint considering uncertainty is equivalent, and the active and reactive output safety constraints of the generator can be equivalent to the following by the formulas (36) and (37):
wherein (sigma P)2、(σQ)2) represents the active and reactive variances of the nodes The column vectors that make up, +..
From the equations (56) and (57), the error of the node voltage and phase angle is expressed as:
εV＝(TP(TQ)-1VQ-VP)-1EPεP-(VQ-TQ(TP)-1VP)-1EQεQ (67)
εθ＝(VP(VQ)-1TQ-TP)-1EPεP-(TQ-VQ(VP)-1TP)-1EQεQ (68)
the voltage safety constraint may be equivalently:
Wherein [ (DEG ] i represents the ith row of the matrix, />I row vectors for the corresponding matrix.
Equation (69) and equation (70) are expressed as a second order taper, as shown in equation (73) and equation (74).
Similarly, the line power error can be expressed by the active and reactive errors as:
The ith row vector of the coefficient matrices ε P and ε Q in equation (75) is denoted as />The safety constraint expression of the line power is shown in the formula (76) and the formula (77), and the second order cone form is shown in the formula (78) and the formula (79).
By the expression, when the variance is fixed, the optimal power flow model is a second order cone optimization problem, the method can be directly solved, and when the variance is an uncertain quantity, the worst variance value is substituted, so that the result of the complete distribution robust model is obtained.
The variance processing process is as follows:
let node i error of history record be The true variance is (σ i)2, estimated variance is/> Since the error obeys a normal distribution expected to be 0, an estimate of the variance can be found from the minimum variance unbiased estimate, as shown in equation (80).
Since the number of historical data satisfies T < ≡, variance estimationThere is still an error, and from the normal distribution obeyed by the active error of the same node, it can be known that/>Obeying the chi-square distribution with the degree of freedom of T, so that the value probability of sigma i)2 is not less than the interval/> of 1-eta σ The upper and lower boundaries of the interval are shown in formula (81).
Wherein,Is 1-eta quantile distributed by chi-square with the degree of freedom of T.
As the historical data increases, the value interval of the variance is reduced, and the variance is maximized under the worst condition of the security constraint of uncertaintySafety constraints are most difficult to meet when this is the case. The second order cone model of DR-SOC-ACOPF is finally obtained as follows:
/>
Wherein (J P)2、(JQ)2) represents the upper bound of the active and reactive variances of the nodes The column vector, J P、JQ, represents the node active and reactive standard deviation upper bound/>A column vector of components.
The invention uses a plurality of IEEE computing examples as the main computing example for verifying the SOC-ACOPF, adjusts the IEEE57 node computing example, and analyzes the computing effect of the DR-SOC-ACOPF. The calculated results of the calculated IEEE57 node are shown in fig. 2, and the calculated generator output of the calculated IEEE 1354 node is shown in fig. 3 and 4, so that the invention has better accuracy. In order to verify the invention, 23 nodes considering uncertainty are arranged in an example, the uncertainty comprises active and reactive fluctuation, the mean value of the fluctuation is 0, the standard deviation is a load value of 0.1 times, the loss sensitivity is 0.05, the number of samples is T=900, as the basis of model solving, the proportion of the generator to power fluctuation allocation is calculated and obtained as shown in figure 5, the uncertainty of the power allocation of the No. 2,4 and 6 groups with the output reaching the limit is avoided, and the proportion of the power allocation of the No. 5 group with the lowest cost is maximized. Thus optimizing economy while ensuring safety. Fig. 6 is a box diagram of voltage amplitude values under different safety constraint probabilities, which is used for describing the quality of the voltage, and it can be seen that the higher the probability of safety requirement is, the higher the voltage quality of the system is. And an additional 600 new random sample verification calculations are generated. The pre-measurement and power fluctuation allocation ratio calculated by the model is combined with new random sample data to simulate, and the number of samples violating the safety constraint is calculated, as shown in fig. 7, as the probability of the safety constraint increases, the probability of the variance interval increases, and the number of random samples violating the safety constraint decreases. By setting the proper probability, the invention can ensure the safety of the result, and the solution of the optimization problem adopts Gurobi solver under MATLAB environment.
The protective scope of the invention is not limited to the embodiments described above, but it is intended that the invention cover modifications and variations of this invention, provided they come within the scope of the appended claims and their equivalents, for those skilled in the art.
Claims (5)
1. The second order cone optimal power flow model and solving method based on distribution robustness is 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 an auxiliary variable, wherein relaxation is a second-order cone constraint, so as to construct a second-order cone optimal power flow model, and meanwhile, adding a relaxation upper limit constraint to limit errors when a relaxation condition is not established;
2) The node power fluctuation considers the prediction deviation of new energy and load, the nonlinear part of the second order cone optimal power flow model is subjected to Taylor expansion, the relation equation between uncertain quantities in the second order cone optimal power flow model is deduced by combining the prediction deviation, expressions of all uncertain quantities are given, and a second order cone optimal 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 tide equation into the linear part and the 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 taken as a linear part, the impedance loss part is taken 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):
Wherein V i and θ i are the voltage amplitude and phase angle of node i; g ij、bij is the conductance and susceptance of the power transmission element i-j;
the expression of the second order cone constraint in step 1) is:
2. the distributed robust second order cone optimal power flow model and solving method according to claim 1, wherein the expression of the error in step 1) is:
3. the distributed-robustness-based second order cone optimal power flow model and solving method according to claim 1, wherein in the step 2), the prediction bias of the new energy and the load is:
Wherein, Representing predicted power of bus i,/>Representing the active and reactive prediction errors.
4. The distribution-robust-based second order cone optimal power flow model and solving method according to claim 1, wherein the variance interval estimation result is:
the active and reactive output safety constraint of the generator can be equivalently:
the voltage safety constraint may be equivalently:
The safety constraints of line power are:
5. the distributed robust second order cone optimal power flow model and solving method according to claim 1, wherein the distributed robust second order cone optimal power flow problem second order cone optimal model is:
Wherein (J P)2、(JQ)2) represents the upper bound of the active and reactive variances of the nodes The column vector, J P、JQ, represents the node active and reactive standard deviation upper bound/>A column vector of components.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010879359.6A CN111985720B (en) | 2020-08-27 | 2020-08-27 | Second order cone optimal power flow model and solving method based on distribution robustness |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010879359.6A CN111985720B (en) | 2020-08-27 | 2020-08-27 | Second order cone optimal power flow model and solving method based on distribution robustness |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111985720A CN111985720A (en) | 2020-11-24 |
| CN111985720B true CN111985720B (en) | 2024-05-28 |
Family
ID=73439974
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010879359.6A Active CN111985720B (en) | 2020-08-27 | 2020-08-27 | Second order cone optimal power flow model and solving method based on distribution robustness |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111985720B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113110561B (en) * | 2021-05-24 | 2021-11-12 | 四川大学 | Random distribution robust optimization-based SMPC algorithm for maintaining formation of satellite |
| CN116455439B (en) * | 2023-06-15 | 2023-10-10 | 南京邮电大学 | Unmanned aerial vehicle communication robust beam forming method based on second-order angle error approximation |
| CN117117973B (en) * | 2023-10-24 | 2024-01-12 | 国网浙江省电力有限公司宁波供电公司 | Distributed power supply scheduling method and device based on time scale and storage medium |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107123988A (en) * | 2017-05-12 | 2017-09-01 | 南京理工大学 | One kind considers that the uncertain power failure network load of amount of recovery recovers Second-order cone programming method |
| CN110137970A (en) * | 2019-05-28 | 2019-08-16 | 华中科技大学 | One kind is based on pyramid approximately without relaxation trend acquisition methods |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7401041B2 (en) * | 2000-12-15 | 2008-07-15 | The Trustees Of Columbia University | Systems and methods for providing robust investment portfolios |
-
2020
- 2020-08-27 CN CN202010879359.6A patent/CN111985720B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107123988A (en) * | 2017-05-12 | 2017-09-01 | 南京理工大学 | One kind considers that the uncertain power failure network load of amount of recovery recovers Second-order cone programming method |
| CN110137970A (en) * | 2019-05-28 | 2019-08-16 | 华中科技大学 | One kind is based on pyramid approximately without relaxation trend acquisition methods |
Non-Patent Citations (2)
| Title |
|---|
| 基于二阶锥优化的含有载调压变压器主动配电网最优潮流;刘斌等;电力系统自动化;第第39卷卷(第第19期期);全文 * |
| 电力系统线性化动态最优潮流模型;赵静波;卫志农;刘建坤;张清松;王大江;;电力系统自动化(第20期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111985720A (en) | 2020-11-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111985720B (en) | Second order cone optimal power flow model and solving method based on distribution robustness | |
| Li et al. | Design of minimum cost degradation-conscious lithium-ion battery energy storage system to achieve renewable power dispatchability | |
| Abedini et al. | Optimal management of microgrids including renewable energy scources using GPSO-GM algorithm | |
| Sossan et al. | Achieving the dispatchability of distribution feeders through prosumers data driven forecasting and model predictive control of electrochemical storage | |
| CN110601252B (en) | MPC-based feeder-level rapid voltage control method for distribution-type photovoltaic power distribution network | |
| Ahmadi et al. | Information-gap decision theory for robust security-constrained unit commitment of joint renewable energy and gridable vehicles | |
| Hu et al. | Intrusion-detector-dependent distributed economic model predictive control for load frequency regulation with PEVs under cyber attacks | |
| Rahmani-Andebili | Cooperative distributed energy scheduling in microgrids | |
| Guo et al. | Sizing energy storage to reduce renewable power curtailment considering network power flows: a distributionally robust optimisation approach | |
| Liu et al. | A robust strategy for leveraging soft open points to mitigate load altering attacks | |
| Ding et al. | IOT-based social-economic management of distribution system with the high penetration of renewable energy sources | |
| Voropai et al. | Intelligent control and protection in the Russian electric power system | |
| Liu et al. | A Mixed integer linear programming‐based distributed energy management for networked microgrids considering network operational objectives and constraints | |
| Ayvaz et al. | Information‐gap decision theory based transient stability constrained optimal power flow considering the uncertainties of wind energy resources | |
| Olfatinezhad et al. | Flexible two‐stage robust model for moving the transmission and reactive power infrastructures expansion planning towards power system integration of renewables | |
| Jeong et al. | Robust prequalification process of a distribution system operator considering N‐1 contingency | |
| CN114757548A (en) | Wind power energy storage equipment adjusting performance evaluation method adopting scene construction | |
| CN114006410A (en) | Large-scale offshore wind power access point optimization method based on opportunity constraint planning | |
| Cañadillas et al. | EDA‐based optimized global control for PV inverters in distribution grids | |
| Dinkelbach et al. | Hosting capacity improvement unlocked by control strategies for photovoltaic and battery storage systems | |
| Ashoornezhad et al. | Optimal Siting and Sizing of Distributed Generation Under Uncertainties Using Point Estimate Method | |
| Xiong et al. | Multi-stage risk-based assessment for wind energy accommodation capability: A robust and non-anticipative method | |
| Sarikprueck | Forecasting of wind, PV generation, and market price for the optimal operations of the regional PEV charging stations | |
| Tukkee et al. | Optimal performance of stand-alone hybrid microgrid systems based on integrated techno-economic-environmental energy management strategy using the grey wolf optimizer | |
| CN113780722B (en) | Joint planning method and device for power distribution network, computer equipment and storage medium |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant |