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.
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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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