Copula method-based independent variable form selection method for linear power flow model

A technology of power flow model and independent variable, applied in the field of independent variable form selection of linear power flow model, which can solve the problems of calculation process oscillation, inability to guarantee the global optimum of optimization results, and inability to compare horizontally.

Pending Publication Date: 2020-11-10
CHONGQING UNIV +2
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Problems solved by technology

In actual calculations, there are often oscillations in the calculation process or even non-convergence
2) The optimal power flow problem is a non-convex large-scale nonlinear programming problem with continuous variables and discrete variables, so the power flow equation will not converge to the final solution, and the global optimum of the optimization result cannot be guaranteed
Its state variables are based on abstract functional functions, so it is impossible to compare existing methods horizontally, and it is difficult to propose the optimal independent variable function form
In fact, the previous theories only discussed the influence of the selection of the state variable function form on the optimal linear approximation model when the state variable distribution function is given, but failed to give the relevant distribution of the state variable v and θ to the power flow equation Impact

Method used

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  • Copula method-based independent variable form selection method for linear power flow model
  • Copula method-based independent variable form selection method for linear power flow model
  • Copula method-based independent variable form selection method for linear power flow model

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Experimental program
Comparison scheme
Effect test

Embodiment 1

[0092] see Figure 1 to Figure 7 , the independent variable form selection method of linear power flow model based on the Copula method, including the following steps:

[0093] 1) Set the nonlinear voltage amplitude term as v i v j .

[0094] 2) Establish nonlinear voltage amplitude term v i v j The state variable function of

[0095] state variable function The normalization conditions are as follows:

[0096]

[0097]

[0098] Among them, the formula (1) represents the state variable function The shrinkage of , the formula (2) expresses the state variable function the translation. is a state variable function first-order guide of .

[0099] state variable function Including the following five forms:

[0100] I) polynomial form: k is an exponent.

[0101] II) Logarithmic form:

[0102] III) Exponential form:

[0103] IV) Trigonometric function form:

[0104] V) Inverse trigonometric function form:

[0105] 3) Calculate the function of v...

Embodiment 2

[0160] The method for selecting the independent variable form of the linear power flow model based on the Copula method includes the following steps:

[0161] 1) Determine the voltage amplitude item The functional form is divided into the following three steps.

[0162] 1.1) The normalization condition

[0163] There are countless functional forms of independent variables. In order to simplify the analysis, we use A normalization condition is proposed, namely and Make Equal to the value of the state variable when v=1; Represents the exponential term of the state variable function. Essentially, and The value of the function shrinkage and translation. It facilitates the analysis without compromising the generality of the proposed method. The present invention has studied The following five forms of (as shown in Table 1), which provide a broad space for finding the minimized linearization error.

[0164] Table 1 different forms of

[0165]

[0166] ...

Embodiment 3

[0197] The experiment of the independent variable form selection method of the linear power flow model based on the Copula method includes the following steps:

[0198] 1) Build a test system: IEEE 118 standard calculation example, v i ,v j All obey the uniform distribution range (0.75p.u., 1.25p.u.), v i ,v j The specific value of is obtained by random sampling

[0199] 2) Verify the algorithm for selecting the optimal Copula function: first calculate the parameters ρ, v and θ of the five Copula functions in Table 3. Then, the Euclidean distances of the five theoretical Copula functions and the empirical Copula functions are shown in Table 4.

[0200] Table 4 Euclidean distance of five Copula functions

[0201] Copula function Euclidean distance Normal 0.0239 t 0.0262 Gumbel 0.0342 Clayton 0.0428 Frank 0.0242

[0202] Figure 3-7 Each subplot in , respectively, embodies the probability density functions represented by the fi...

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Abstract

The invention discloses a Copula method-based independent variable form selection method for a linear power flow model. The method comprises the following steps of: 1) setting a nonlinear voltage amplitude item as vivj; 2) establishing a state variable function of a non-linear voltage amplitude item vivj; 3) calculating a linearization error function of the non-linear voltage amplitude item vivj under different state variable functions; 4) simulating numerical joint probability distribution of state variables of the power flow equation by using a Copula function analysis method, and establishing a Copula optimization model; and 5) based on the linearization error function of the non-linear voltage amplitude item vivj and the Copula optimization model, establishing a linear power flow modelwith the minimum error. According to the method, the linearization error of vivj under different formulas is discussed, the joint probability density function is fitted through the Copula function, the minimized linearization error is obtained, and then the power flow model with the minimum error is established.

Description

technical field [0001] The invention relates to the field of power flow optimization, in particular to a method for selecting independent variable forms of a linear power flow model based on a Copula method. Background technique [0002] Power system power flow calculation is a basic electrical calculation for power system steady-state analysis based on the independent variable form selection method of the linear power flow model based on the Copula method. The expression of the power flow equation is as follows: [0003] P ij (v,θ ij ) = g ij (v i 2 -v i v j cosθ ij )-b ij v i v j sinθ ij (1) [0004] Q ij (v,θ ij )=-b ij (v i 2 -v i v j cosθ ij )-g ij v i v j sinθ ij (2) [0005] Due to the nonlinear characteristics of the power flow equation, there are the following two problems: 1) The nonlinear equations of the power flow equation have NP-hard problems. In actual operation, the oscillation or even non-convergence of the calculation process of...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/20G06F17/18G06F111/04G06F111/10
CPCG06F17/18G06F30/20G06F2111/04G06F2111/10
Inventor 杨知方樊哲新余娟杨燕余红欣王洪彬冯楠姜华
Owner CHONGQING UNIV
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