CN116526489A - Power distribution network power flow uncertainty analysis method considering uncertainty factor correlation - Google Patents
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Abstract
The invention discloses a power flow uncertainty analysis method of a power distribution network considering uncertainty factor correlation, and relates to the field of power distribution networks.
Description
Technical Field
The invention relates to the field of power distribution networks, in particular to a power distribution network power flow uncertainty analysis method considering uncertainty factor correlation.
Background
In recent years, environmental problems caused by large carbon emissions are increasingly serious, and promotion of development of clean energy is of great significance. However, the intermittent performance and the fluctuation of the output of clean energy sources such as solar energy, wind energy and the like are strong, so that the safe and stable operation of the power distribution network can be threatened when the clean energy sources are accessed on a large scale. Therefore, it is increasingly important to study the influence of uncertainty factors such as distributed generation output on the power flow of the power distribution network to maintain stable operation of the power distribution network.
The prior research proposes that a global sensitivity analysis method (Global Sensitivity Analysis, GSA) is used for carrying out influence analysis on uncertainty factors such as photovoltaic output, wind turbine output, load and the like. The method measures the effect of uncertainty factors on system output (e.g., frequency or voltage) by evaluating metrics including a First-order sensitivity metric (FSI) and a total sensitivity metric (Total Sensitivity Index, TSI). Wherein FSI represents the influence of the uncertainty factor itself on the system output, while TSI represents the common influence of the uncertainty factor itself and interactions with other uncertainty factors on the system output. For independent uncertainty factors, its TSI is always greater than its FSI. By ordering the TSI and FSI, key uncertainty factors that affect system stability can be obtained. However, when there is correlation between uncertain factors (for example, the output of wind turbines with similar distances in a power distribution network has stronger correlation), TSI and FSI obtained based on the traditional GSA method have larger phase difference, so that the situation of contradiction can occur between the FSI and TSI sequencing results based on the uncertain factors, and key uncertain factors affecting the safe and stable operation of the system cannot be finally determined.
Disclosure of Invention
The invention aims to provide a power distribution network trend uncertainty analysis method considering uncertainty factor correlation, which is used for determining the importance degree of an input random variable by evaluating the average marginal contribution of the input random variable to output variable fluctuation, and quantitatively evaluating the influence of the uncertainty factors on the output variables such as system frequency, node voltage amplitude, active power of a line and the like when the output of a distributed power generation device such as a photovoltaic generator set and the like and the load in a power distribution network have correlation, so as to obtain key uncertainty factors influencing the safe and stable operation of the power distribution network, and solve the problems in the background technology.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a power distribution network power flow uncertainty analysis method considering uncertainty factor correlation comprises the following steps:
(1) the power flow uncertainty analysis method of the power distribution network is used for identifying key uncertainty factors influencing the running state of the power distribution network by calculating global sensitivity indexes of all uncertainty factors. The uncertainty factors include random renewable energy source generation power and power load at different network nodes of the power distribution network, and the global sensitivity index is obtained by calculating a global sensitivity analysis (Global sensitivity analysis, GSA) method based on Shapley values.
(2) The Shapley-based global sensitivity analysis (Global sensitivity analysis, GSA) method is described as follows: let xi= (xi) 1 ,ξ 2 ,…,ξ N ) Independent input random variable for N dimension, Y=g (ζ) is defined in Ω N Square integrable function of space, where Ω N Can be expressed as omega N ＝{ξ|0≤ξ i Not more than 1, i=1, 2,..n }. From a High-dimensional model representation of the function (High-dimensional Model Representation, HDMR), g (ζ) can be decomposed into 2 k Sum of term integrable functions: wherein: g i ＝g i (x i )，g ij ＝g ij (ξ i ,ξ j )，g 12…N ＝g 12…N (ξ 1 ,ξ 2 ,…,ξ N ) Other higher order decomposition terms may be similarly represented; g 0 Is constant. For a given function y=g (ζ), the above-described function-based high-dimensional model represents the decomposition uniqueness theorem that follows in the presence of the decomposition of HDMR, the total variance of the function y=g (ζ) can be expressed as: />The bias variance can be expressed as: />If xi is the unit body space omega N Random variables uniformly distributed on the upper part, g (ζ) and g m…n Variance is D and D respectively m…n To obtain a high-dimensional model representation of analysis of variance (ANOVA-HDMR): />
(3) The global sensitivity index was defined according to ANOVA-HDMR as: s is S m…n ＝D m…n and/D. Wherein: s is S i Is xi i First-order Sensitivity Index, FSI; at the same time define xi i The overall sensitivity index (Total Sensitivity Index, TSI) of (a) is:
(4) based on the result of variance decomposition, the input variable xi is obtained i The first order sensitivity index FSI and the total sensitivity index TSI of (a) are as follows: s is S i ＝D i /D；S T,i ＝1-D ～i and/D, wherein: d (D) ～i For all ofAnd (3) summing;
(5) the average marginal contribution of the input random variable to the fluctuation of the output variable is evaluated based on the Shapley value. Definition x i Shapley Value-based Global Sensitivity Index, SVGSI): wherein c (x l ) Defined in the present invention as the input set of random variables x as a cost function l TSI, & gt>z is the division of x l A set of other input random variables; w (x) l ) To input random variable x l Corresponding weight coefficient, w (x l )＝(N-|x l |-1)！|x l |！/N！，|x l I is x l The number of input random variables contained in the table. Whether or not the cost function c (x l ) Defined as x l Is also FSI, x obtained by GSA method based on Shapley value i The sensitivity index of the system is unchanged, so that the situation that the first-order sensitivity index TSI and the total sensitivity index FSI are mutually contradictory when the importance of the input random variable is evaluated under the condition that the correlation exists between uncertainty factors is solved, and the key uncertainty factors of the system can be identified more accurately and effectively;
(6) and acquiring key uncertainty factors affecting safe and stable operation of the power distribution network according to the SVGSI sequencing result of the input variables from high to low.
Compared with the prior art, the invention has the beneficial effects that: the invention determines the importance degree of the input random variable by evaluating the average marginal contribution of the input random variable to the fluctuation of the output variable, and defines the global sensitivity index based on the Shapley value. When the correlation exists between uncertainty factors, the problem that FSI and TSI are mutually contradictory when the importance of the input random variable is evaluated is solved, so that key uncertainty factors of a system are more accurately and effectively identified, and the safe and stable operation of the power distribution network is supported.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a schematic diagram of a 33-node power distribution network system according to an embodiment of the present invention.
FIG. 3 is a graph showing correlation coefficients between 38 input random variables in an embodiment of the present invention.
FIG. 4 is a schematic diagram of FSI and TSI with independent input of random variables in an embodiment of the present invention.
FIG. 5 is a schematic diagram of FSI and TSI of related input random variables in an embodiment of the present invention.
FIG. 6 is a schematic diagram of FSI, TSI and SVGSI (SV) for random variable input in an embodiment of the invention.
FIG. 7 shows a WT in an embodiment of the invention 1 And WT (WT) 3 FSI, TSI and SVGSI diagrams of output power.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, in the embodiment of the present invention, (1) the power flow uncertainty analysis method of the power distribution network is used for identifying key uncertainty factors affecting the running state of the power distribution network by calculating global sensitivity indexes of all uncertainty factors. The uncertainty factors include random renewable energy source generation power and power load at different network nodes of the power distribution network, and the global sensitivity index is obtained by calculating a global sensitivity analysis (Global sensitivity analysis, GSA) method based on Shapley values.
(2) The Shapley-based global sensitivity analysis (Global sensitivity analysis, GSA) method is described as follows: let ζ= (ζ1, ζ2, …, ζn) be an N-dimensional independent input random variable, y=g (ζ) be a square integrable function defined in Ω N space, where Ω N may be expressed as Ω N ＝{ξ|0≤ξ i Not more than 1, i=1, 2,..n }. From a High-dimensional model representation of the function (High-dimensional Model Representation, HDMR), g (ζ) can be decomposed into the sum of 2 k-term integrable functions: wherein: gi=gi (xi), gij=gij (ζi, ζj), g … n=g … N (ζ1, ζ2, …, ζn), other higher order decomposition terms may be similarly represented; g0 is a constant. For a given function y=g (ζ), the above described HDMR-based decomposition has the following decomposition uniqueness theorem, the total variance of the function y=g (ζ) can be expressed as:the bias variance can be expressed as: /> If ζ is a random variable uniformly distributed over the unit volume space Ω N, g (ζ) and gm … N are random variables with variances D and Dm … N, respectively, so that a high-dimensional model representation of the analysis of variance (ANOVA-HDMR) can be obtained: />
(3) The global sensitivity index was defined according to ANOVA-HDMR as: s is S m…n ＝D m…n and/D. Wherein: first order sensitivity index with Si being xi (First-order sensor sensitivity vity Index, FSI); meanwhile, the total sensitivity index (Total Sensitivity Index, TSI) of ζi is defined as:
(4) further, based on the result of the variance decomposition, FSI and TSI of the input variable ζi are obtained as follows: s is S i ＝D i /D；S T,i ＝1-D ～i and/D. Wherein: d-i is allAnd (3) summing.
(5) Then, the average marginal contribution of the input random variable to the fluctuation of the output variable is evaluated based on the Shapley value. Global sensitivity index based on Shapley values (Shapley Value-based Global Sensitivity Index, SVGSI) defining xi: where c (xl) is a cost function, defined in the present invention as TSI of the input random variable set xl,>z is a set of other input random variables except xl; w (xl) is a weight coefficient corresponding to the input random variable xl, w (x) l )＝(N-|x l |-1)！|x l | is (is) provided! N-! And the xl is the number of input random variables contained in xl. It should be noted that, whether the cost function c (xl) is defined as the TSI or the FSI of xl, the sensitivity index of xi obtained by the GSA method based on the Shapley value is unchanged, so that the problem that the FSI and the TSI are mutually contradictory when evaluating the importance of the input random variable under the condition that there is correlation between uncertainty factors is solved, and the key uncertainty factors of the system are more accurately identified.
(6) And acquiring key uncertainty factors affecting safe and stable operation of the power distribution network according to the SVGSI sequencing result of the input variables from high to low.
As a further embodiment of the present invention, referring to fig. 2, the present embodiment relates to an IEEE 33 node active power distribution system, in which 7 distributed power generation (Distributed generation, DG) devices are connected, the connection nodes are respectively 10, 29, 12, 22, 18, 33 and 25, and include 2 photovoltaic cells (PV), 3 Wind Turbines (WT) 1 And WT (WT) 2 ) And 2 gas turbines (DG) 1 And DG 2 ). The line parameters of 7 DG devices accessing the active power distribution system are shown in table 1:
table 1DG device access to micro grid line data
Wherein DG 1 And DG 2 For the droop control node and adopting a droop control mode of P-f/Q-U, the control parameters are shown in Table 2:
table 2DG device droop control parameters
Wherein, the value of the no-load voltage amplitude and the value of the no-load frequency per unit of the P-f/Q-U droop control mode are U respectively i,2 ＝1.06、f 2 =1.004. The reference frequency of the 33-node power distribution network system is 50Hz, the reference capacity is 1MVA, and the frequency f is set 3 The per unit value of the total load of the system at =1.000p.u. is 3.715+2.3j, the steady-state frequency safety range is 0.996p.u. to 1.004p.u. and the safety range of the node voltage amplitude is 0.94p.u. to 1.06p.u. during normal operation of the system. Considering the source-load uncertainty in the distribution network, the input random variables are 38 (output of 5 DG devices and 33 user loads), and the correlation between the input random variables is described by using a linear correlation coefficient matrix, and the correlation coefficients are shown in fig. 3.
As a further embodiment of the present invention, the present invention provides a power distribution network load flow uncertainty analysis method considering uncertainty factor correlation, including the following steps:
step a) let ζ= (ζ) 1 ,ξ 2 ,…,ξ N ) Independent input random variable for N dimension, Y=g (ζ) is defined in Ω N Square integrable function of space, where Ω N Can be expressed as omega N ＝{ξ|0≤ξ i Not more than 1, i=1, 2,..n }. From a High-dimensional model representation of the function (High-dimensional Model Representation, HDMR), g (ζ) can be decomposed into 2 k Sum of term integrable functions: wherein: g i ＝g i (x i )，g ij ＝g ij (ξ i ,ξ j )，g 12 …N＝g 12…N (ξ 1 ,ξ 2 ,…,ξ N ) Other higher order decomposition terms may be similarly represented; g 0 Is constant. For a given function y=g (ζ), the above described HDMR-based decomposition has the following decomposition uniqueness theorem, the total variance of the function y=g (ζ) can be expressed as:the bias variance can be expressed as: />If xi is the unit body space omega N Random variables uniformly distributed on the upper part, g (ζ) and g m…n Variance is D and D respectively m…n To obtain a high-dimensional model representation of analysis of variance (ANOVA-HDMR): />
Step B) defining global sensitivity indexes according to ANOVA-HDMR as follows: s is S m…n ＝D m…n and/D. Wherein: s is S i Is xi i First-order Sensitivity Index, FSI; at the same time define xi i The overall sensitivity index (Total Sensitivity Index, TSI) of (a) is:
step C) further, obtaining an input variable xi based on the variance decomposition result i The FSI and TSI of (2) are as follows: s is S i ＝D i /D；S T,i ＝1-D ～i and/D. Wherein: d (D) ～i For all ofAnd (3) summing.
Step D) then, estimating the average marginal contribution of the input random variable to the fluctuation of the output variable based on the Shapley value. Definition x i Shapley-based global sensitivity index (SVGSI, shapley value-based Global Sensitivity Index): wherein c (x l ) Defined in the present invention as the input set of random variables x as a cost function l TSI, & gt>z is the division of x l A set of other input random variables; w (x) l ) To input random variable x l Corresponding weight coefficient, w (x l )＝(N-|x l |-1)！|x l |！/N！，|x l I is x l The number of input random variables contained in the table. Whether or not the cost function c (x l ) Defined as x l Is also FSI, x obtained by GSA method based on Shapley value i The sensitivity index of (1) is unchanged, thus solving the problem that FSI and TSI evaluate under the condition that the correlation exists between uncertainty factorsThe contradiction between the importance of the input random variable is estimated, which is beneficial to more accurately and effectively identifying the key uncertain factors of the system.
And E) acquiring key uncertainty factors affecting safe and stable operation of the power distribution network according to the SVGSI sequencing result of the input variables from high to low.
When the correlation between the input random variables is not considered, the GSA method based on conditional variance calculates FSI and TSI of the input random variables as shown in FIG. 4, and numbers 1 to 38 represent WT, respectively 1 -WT 3 ,PV 1 ,PV 2 ,Load 1 -Load 33 The Loads represent the whole of 33 user Loads, and it can be seen that when correlation among input random variables is not considered, FSI and TSI of the input random variables are not greatly different (TSI is slightly larger than FSI), which indicates that interaction of endogenous-load uncertainty factors of a power distribution network system has little influence on the system frequency of the power distribution network, and fluctuation of the system frequency is mainly influenced by independent action of each uncertainty factor.
When considering the correlation between input random variables, FSI and TSI of the input random variables are obtained using the GSA method based on conditional variance as shown in FIG. 5, with numbers 1-38 representing WT, respectively 1 -WT 3 ,PV 1 ,PV 2 ,Load 1 -Load 33 Loads represents the whole of 33 user Loads
It can be seen that when considering the correlation between the input random variables, the different input random variables FSI and TSI result are very different.
Based on the FSI and TSI results for the input random variables, table 3 gives the importance ranking results for the relevant input random variables:
TABLE 3 input random variable importance ordering based on FSI and TSI
It can be seen that FSI is greater than TSI when considering the correlation between input random variables, and that in combination with Table 3, the result of ranking the importance of the input random variables based on FSI can be seenThere is some deviation from the results obtained based on TSI. In particular, when the system frequency is used as the output variable, the PV is known from the ordering of FSI 1 The variation of the output power has the greatest influence on the fluctuation of the active power transmitted by the line 6-7; while the WT is known from the ordering result of the TSI 2 The variation of the output power has the greatest influence on the fluctuation of the active power transmitted by the line 6-7, whereas the PV 1 The influence of output power is minimum, and the identification results of the two indexes are contradictory.
Next, SVGSI of the input random variable is calculated using Shapley-based GSA method and compared with FSI, TSI. Changing the WT while maintaining the correlation coefficient between other input random variables unchanged 1 And WT (WT) 3 Correlation coefficient ρ between output powers 13 The resulting FSI, TSI and SVGSI input random variables are shown in FIGS. 6 and 7.
From fig. 6 and 7, it can be seen that any SVGSI that inputs random variables is between its FSI and TSI, and the nature of the combined SVGSI is known to be a compromise between FSI and TSI. With WT 1 And WT (WT) 3 Correlation coefficient ρ between output powers 13 Augmentation, WT 1 And WT (WT) 3 FSI of (C) gradually increases and tends to be the same value, while TSI gradually decreases and approaches 0, and WT is known after SVGSI compromise 1 And WT (WT) 3 The effect of variations in output power on system frequency fluctuations is a function of ρ 13 Is slightly increased.
The algorithm is original for the invention, is never disclosed, and the working mode is different from any existing literature record: the invention determines the importance degree of the input random variable by evaluating the average marginal contribution of the input random variable to the fluctuation of the output variable, and defines the global sensitivity index based on the Shapley value. When the correlation exists between uncertainty factors, the problem that FSI and TSI are mutually contradictory when the importance of the input random variable is evaluated is solved, so that key uncertainty factors of a system are more accurately and effectively identified, and the safe and stable operation of the power distribution network is supported.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.
Claims (1)
1. The power distribution network power flow uncertainty analysis method considering uncertainty factor correlation is characterized by comprising the following steps of:
(1) the power flow uncertainty analysis method of the power distribution network is used for identifying key uncertainty factors influencing the running state of the power distribution network by calculating global sensitivity indexes of all uncertainty factors, wherein the uncertainty factors to be considered comprise random renewable energy power generation power and power load of different network nodes of the power distribution network, and the global sensitivity indexes are calculated and obtained by adopting a global sensitivity analysis method based on Shapley values;
(2) the global sensitivity analysis method based on Shapley values is described as follows: let xi= (xi) 1 ，ξ 2 ，...，ξ N ) Independent input random variable for N dimension, Y=g (ζ) is defined in Ω N Square integrable function of space, where Ω N Represented as omega N ＝{ξ|0≤ξ i Not more than 1, i=1, 2, N, from the high-dimensional model HDMR representation of the function, decomposing g (ζ) into 2 k Sum of term integrable functions:wherein: g i ＝g i (x i )，g ij ＝g ij (ξ i ，ξ j )，g 12...N ＝g 12...N (ξ 1 ，ξ 2 ，...，ξ N ) Other higher order decomposition terms are similarly represented; g 0 For a constant, for a given function y=g (ζ), the decomposition of the above-described function-based high-dimensional model HDMR has the following decomposition uniqueness theorem, the total variance of the function y=g (ζ) expressed as: the bias is expressed as: />ζ is the unit body space Ω N Random variables, g (ζ) and g, uniformly distributed on the surface m...n Variance is D and D respectively m...n To obtain a high-dimensional model representation of the analysis of variance (ANOVA-HDMR): />
(3) The global sensitivity index was defined according to ANOVA-HDMR as: s is S m…n ＝D m…n /D, wherein: s is S i Is xi i First order sensitivity index FSI; at the same time define xi i The total sensitivity index TSI of (a) is:
(4) based on the result of variance decomposition, the input variable xi is obtained i The first order sensitivity index FSI and the total sensitivity index TSI of (a) are as follows: s is S i ＝D i /D；S T，i ＝1-D ～i and/D, wherein: d (D) ～i For all ofAnd (3) summing;
(5) estimating the average marginal contribution of the input random variable to the fluctuation of the output variable based on the Shapley value, and defining x i Is based on the global sensitivity index SVGSI of Shapley value:wherein c (x l ) Is defined as a set x of input random variables as a cost function l TSI, & gt>z is the division of x l A set of other input random variables; w (x) l ) To input random variable x l Corresponding weight coefficient, w (x l )＝(N-|x l |-1)！|x l |！/N！，|x l I is x l The number of input random variables included in (a) no matter how many the cost function c (x l ) Defined as x l Is also the first-order sensitivity index TSI or the total sensitivity index FSI, x is obtained by the GSA method based on Shapley value i The sensitivity index of (2) is unchanged;
(6) and acquiring key uncertainty factors affecting safe and stable operation of the power distribution network according to the SVGSI sequencing result of the input variables from high to low.
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