CN-121996879-A - Event constraint unit combination robust optimization solving method based on basis function self-adaptive chaos polynomial expansion

CN121996879ACN 121996879 ACN121996879 ACN 121996879ACN-121996879-A

Abstract

The invention discloses an event constraint unit combination robust optimization solving method based on basis function self-adaptive chaos polynomial expansion, which comprises the following steps of 1) establishing an event constraint unit combination robust optimization model, wherein the event constraint unit combination robust optimization model comprises a daily unit combination model and a state evaluation model under a composite scene considered, 2) approximating the state evaluation model by adopting the basis function self-adaptive sparse chaos polynomial expansion, constructing a state evaluation proxy model, 3) replacing the state evaluation model in the unit combination robust optimization model by adopting the state evaluation proxy model, and 4) solving the replaced unit combination robust optimization model to obtain a unit combination scheme. According to the invention, the state evaluation model is reconstructed through a relaxation technology to improve the smoothness of model response, and on the basis, a proxy model of the state evaluation model is built based on BASPCE, so that the accuracy of the proxy model is remarkably improved.

Inventors

TANG JUNJIE
SUN QING
WANG YUZHI
LIN XINGYU
WANG JUNZHOU
ZHAO ZIWEI
ZHANG YILIN

Assignees

重庆大学

Dates

Publication Date: 20260508
Application Date: 20251217

Claims (10)

1. The event constraint unit combination robust optimization solving method based on the basis function self-adaptive chaos polynomial expansion is characterized by comprising the following steps of: Step 1), establishing an event-constrained unit combination robust optimization model, wherein the event-constrained unit combination robust optimization model comprises a daily unit combination model and a state evaluation model under a consideration composite scene; Step 2) adopting self-adaptive sparse chaos polynomial expansion to approximate a state evaluation model, and constructing a state evaluation proxy model; step 3) replacing a state evaluation model in the unit combination robust optimization model by using a state evaluation agent model; and 4) solving the replaced unit combination robust optimization model to obtain a unit combination scheme.
2. The method for combined robust optimization solution of event constraint unit based on basis function adaptive chaos polynomial expansion according to claim 1, wherein in step 1), the optimization objective of the combined robust optimization model is to minimize the cost in the worst case; the objective function of the set-up robust optimization model is as follows: ;(1) Wherein z and y respectively represent a daily unit combination model and a state evaluation model decision variable set, f UC represents an operation cost function in the system base state operation, omega C and omega S respectively represent a system element fault scene set and a source load prediction error scene set, and k and s respectively represent indexes thereof; G k and l k respectively represent state matrixes of a system unit and a line in a fault scene k, wherein 1 represents that an element is in an operation state, and 0 represents that the element is in a fault shutdown state; And The load prediction error and the new energy prediction error in the prediction error scene s are respectively represented.
3. The method for solving the event constraint unit combination robust optimization based on basis function self-adaptive chaos polynomial expansion according to claim 1, wherein the objective function of a day-ahead unit combination model is as follows: ;(2) Wherein f OC ,f SSC and f SRC respectively represent the running cost, start-stop cost and rotation standby cost of the generator, a Q,g ,a L,g and a C,g respectively represent the secondary term, primary term and constant term of the generation cost coefficient of the generator g, auxiliary variables C SU,g,t and C SD,g,t respectively represent the cost of the generator g generated by start-up and stop at time t, a R,g represents the standby cost coefficient of g, omega B ,Ω G and omega L respectively represent the bus, g and ij respectively, t and k respectively represent the indexes of the scheduling period and the system element fault scene, and z= { u g,t ,P G,g,t ,R g,t ,C SU,g,t ,C SD,g,t ,θ i,t | U g,t represents the start-stop state of the generator g at the time t, 1 represents the running state of the generator, 0 represents the stop operation, P G,g,t and R g,t respectively represent the output and standby of the generator g at the time t, and θ i,t represents the phase angle of the bus i at the time t.
4. The method for solving the event constraint unit combination robust optimization based on basis function self-adaptive chaos polynomial expansion according to claim 1, wherein the constraint conditions of a day-ahead unit combination model are as follows: ;(3) ;(4) ;(5) ;(6) ;(7) ;(8) ;(9) ;(10) ;(11) ;(12) ;(13) Wherein the constraints (3) - (5) represent direct current power flow constraints, P D,i,t represents the active predicted load of the bus i at the time t, P ij,t and theta ij,t respectively represent the active power and phase angle difference of the line ij at the time t, X ij represents the reactance of the line ij, Representing the maximum active power allowed by the line ij, the subscript 'ref' represents the balancing node, and the constraint (6) is the upper and lower limit constraints of the generator output, wherein, And The method is characterized by comprising the steps of respectively representing minimum output and maximum output of a generator, wherein constraint (7) is a climbing and landslide constraint of the generator, r DN,g and r UP,g respectively represent a landslide rate and a climbing rate of the generator g, constraint (8) is a reserve capacity constraint of the generator, constraint (10) and constraint (11) are minimum starting and stopping time constraint of the generator, DT g and UT g respectively represent minimum stopping time and minimum running time of the generator g, tau is an auxiliary variable, and constraint (12) and constraint (13) respectively represent starting cost and stopping cost of the generator g at a moment t.
5. The method for combined robust optimization solution of event constraint unit based on basis function adaptive chaos polynomial expansion according to claim 1, wherein for the following steps of , The objective function of the state estimation model under the composite scene is considered as follows: ;(14) Where a LS,i represents the load shedding cost factor of bus i, and y= { | }, Wherein , And Respectively representing the output of the generator g, the load of the bus i and the phase angle under the compound scene (k, s); The tangential load of the busbar i at time t under the composite scene (k, s) is shown.
6. The method for combined robust optimization solution of the event constraint unit based on basis function adaptive chaos polynomial expansion according to claim 1, wherein constraint conditions of a state evaluation model under a composite scene are as follows: ;(15) ;(16) ;(17) ;(18) ;(19) ;(20) Wherein, the constraints (15) - (17) represent direct current power flow constraints, wherein, And The active power flow and phase angle difference of a line ij under a composite scene (k, s), the constraint (18) is the active load constraint of a bus i, the constraint (19) is the active power output upper and lower limit constraint of a generator, and the constraint (20) is the climbing constraint of the generator.
7. The method for combined robust optimization solution of an event constraint unit based on basis function adaptive chaotic polynomial expansion according to claim 1, wherein in the step 2), the step of approximating the state evaluation model by adopting the basis adaptive sparse chaotic polynomial expansion comprises the following steps: step 2.1) determining random input of a state evaluation model, wherein the random input comprises a daily unit combination decision and a source load prediction error, and the daily unit combination decision comprises a unit start-up and stop state, unit output and unit standby; Step 2.2) setting probability density distribution of a combination decision of a unit before the day, converting a source load prediction error history sample obeying any distribution into an experimental design sample for constructing a proxy model by adopting a Gaussian-copula model, and determining the probability density distribution of the experimental design sample; Step 2.3) selecting an orthogonal basis function for approximating the random input according to the probability density distribution type of the random input; The orthogonal basis function is a Legendre polynomial if the probability density distribution type is uniform distribution, a Hermite polynomial if the probability density distribution type is normal distribution, a Laguerre polynomial if the probability density distribution type is Gamma distribution, and a Jacobi polynomial if the probability density distribution type is Beta distribution; step 2.4) relaxing the upper bound of the node load to obtain: ;(21) in the formula, Is far greater than For effecting relaxation of node loads; step 2.5) evaluating the proxy model based on the build state, namely: ;(22) ;(23) Wherein D k represents a set of proxy models under k in a fault scene, including the proxy model of each period K and s represent the fault scene vector and the source load prediction error scene vector, respectively.
8. The method of claim 7, wherein in the step 2.2), for the machine set start-stop state u and the machine set output P G , a complex variable u.P G is constructed, and the complex variable u.P G is set to obey [0, Uniformly distributed, and for unit reserve R G , setting unit reserve R G to obey [0, Uniform distribution of ].
9. The method for combined robust optimization solution of event constraint unit based on basis function adaptive chaos polynomial expansion according to claim 7, wherein in step 2.2), the step of converting the source load prediction error history samples subject to arbitrary distribution into experimental design samples for constructing a proxy model comprises: Step 2.2.1) calculating a spearman rank correlation coefficient matrix C S,O according to historical samples of random variables; The Spearman correlation coefficient matrix in standard gaussian space satisfies the following equation: ;(24) Step 2.2.2) constructing a Pearson correlation coefficient matrix C P,Z corresponding to the standard Gaussian space based on the conversion relation between the Pearson correlation coefficient and the Spearman correlation coefficient in the Gaussian variable, namely: ;(25) Step 2.2.3) performing Cholesky decomposition on the pearson correlation coefficient matrix C P,Z to obtain: ;(26) Wherein L is a lower triangular matrix; step 2.2.4) independent samples generated by Latin hypercube sampling Construction of a correlation Standard Gaussian sample The method comprises the following steps: ;(27) step 2.2.5) correlating Gaussian samples by inverse probability transformation Mapping to original domain, generating original domain sample The method comprises the following steps: ;(28) Where phi represents a standard Gaussian cumulative distribution function, The distribution function is accumulated for the inverse of the mth random variable in the original domain.
10. The method for solving the event constraint unit combination robust optimization based on basis function adaptive chaos polynomial expansion according to claim 1, wherein in the step 4), the step of solving the replaced unit combination robust optimization model comprises the following steps: Step 4.1) adding constraint cost variable constraints of each fault scene in the daily-life unit combination model: ;(29) ;(30) Step 4.2) reconstructing the unit combination robust optimization model into a min-max problem, namely: ;(31) Wherein d represents a set of auxiliary variables; Step 4.3) introducing an independent source load scene decision variable set s k for each fault scene k, and reconstructing the min-max double-layer optimization problem into a single-layer minimization problem, namely: ;(32) Wherein S k represents a set of source load prediction error decision variables under the fault scene k, and S represents a box type uncertainty set of source load prediction errors; And 4.4) solving a single-layer minimization problem through a gurobi solver to obtain a unit combination scheme under the most serious fault scene and the continuous source load uncertainty scene.

Description

Event constraint unit combination robust optimization solving method based on basis function self-adaptive chaos polynomial expansion Technical Field The invention relates to the field of uncertainty analysis of an electric power system, in particular to an event constraint unit combination robust optimization solving method based on basis function self-adaptive chaos polynomial expansion. Background In recent years, a power system uncertainty analysis method based on a proxy model is widely focused on balancing calculation efficiency and accuracy, wherein Basis function adaptive chaotic polynomial expansion (basic-ADAPTIVE SPARSE Polynomial Chaos Expansion, BASPCE) is one of hot spots of current research. However, most of the existing optimization models based on BASPCE do not consider operation adjustment measures such as load shedding, and the response behavior of the system under fault or extreme working conditions is difficult to accurately simulate, so that the application in safety and reliability evaluation is still limited. In system state evaluation and risk analysis, cut load quantity indexes often show non-smooth characteristics under uncertain environments, particularly under the scenes of small-capacity unit faults and the like, probability distribution of the cut load quantity indexes is gathered at zero values, and uneven transition exists between the zero values and positive values. This discontinuity in distribution poses a challenge for directly applying the chaotic polynomial expansion model, since the accuracy of such methods depends on the smoothness of the output response. In fact, decision-dependent uncertainties (such as start-stop of a unit, power generation output before the day, standby distribution and the like) existing in the operation of the power system are high-dimensional and complex, and can significantly influence the state evaluation result, and the existing agent model method does not consider the factor. For uncertainty optimization which simultaneously considers source load uncertainty and element fault scenes, the existing research is concentrated on a random optimization framework, conservation consideration of extreme scenes is insufficient, the decision is difficult to ensure to have enough robustness, and the random optimization often causes excessive calculation burden due to scene combination explosion. Robust optimization is another uncertainty optimization method that looks for the most severe uncertainty scenario to guarantee the robustness of the final solution. Conventional robust optimization employs iterative solution methods, such as Column & constraint generation (C & CG) algorithms, but such iterative solution algorithms are time consuming to solve when the uncertainty scenario is large. As described above, the prior art has limitations in terms of processing high-dimensional uncertainty, model non-smooth output and decision-dependent uncertainty, and lacks a solution method capable of efficiently solving a set of combined robust optimization models in a large number of composite scenarios. Disclosure of Invention The invention aims to provide an event constraint unit combination robust optimization solving method based on basis function self-adaptive chaos polynomial expansion, which comprises the following steps: Step 1), establishing an event-constrained unit combination robust optimization model, wherein the event-constrained unit combination robust optimization model comprises a daily unit combination model and a state evaluation model under a consideration composite scene; Step 2) adopting self-adaptive sparse chaos polynomial expansion to approximate a state evaluation model, and constructing a state evaluation proxy model; step 3) replacing a state evaluation model in the unit combination robust optimization model by using a state evaluation agent model; and 4) solving the replaced unit combination robust optimization model to obtain a unit combination scheme. Further, in step 1), the optimization objective of the unit combination robust optimization model is to minimize the cost in the worst case; the objective function of the set-up robust optimization model is as follows: (1) Wherein z and y respectively represent a daily unit combination model and a state evaluation model decision variable set, f UC represents an operation cost function in the system base state operation, omega C and omega S respectively represent a system element fault scene set and a source load prediction error scene set, and k and s respectively represent indexes thereof; G k and l k respectively represent state matrixes of a system unit and a line in a fault scene k, wherein 1 represents that an element is in an operation state, and 0 represents that the element is in a fault shutdown state; And The load prediction error and the new energy prediction error in the prediction error scene s are respectively represented. Further, the objective function of the day-ahead