CN114897414B - Identification method for key uncertain factors of power distribution network containing high-proportion photovoltaic and electric automobile - Google Patents
Identification method for key uncertain factors of power distribution network containing high-proportion photovoltaic and electric automobile Download PDFInfo
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Abstract
A method for identifying key uncertain factors of a power distribution network of an electric automobile with high proportion of photovoltaic and electric automobiles comprises the following steps: inputting a deterministic parameter and a randomness parameter of the power distribution network according to the selected power distribution network; obtaining random variable samples which are independent of each other in a standard normal space, and obtaining random variable samples in a probability space of the power distribution network; establishing a deterministic power flow calculation model of the power distribution network, and obtaining a power distribution network voltage risk index as a target response; establishing an index set of random variables in a probability space of the power distribution network, and dividing a subset and a complement of the random variable index; establishing and solving a low-rank approximation model of the power distribution network voltage risk index; the obtained low-rank approximation model of the power distribution network voltage risk index adopts a global sensitivity analysis method to calculate the global sensitivity of each non-empty subset of random variables in the power distribution network probability space; and identifying key uncertain factors affecting the power distribution network voltage risk index. The invention improves the investment economy and effectively improves the safe operation of the power distribution network.
Description
Technical Field
The invention relates to a method for identifying key uncertain factors of a power distribution network. In particular to a method for identifying key uncertain factors of a power distribution network of an electric automobile with high proportion of photovoltaic and electric vehicles.
Background
In order to promote clean transformation and upgrading of the power system, the power distribution network becomes a main platform for distributed photovoltaic digestion. However, after the photovoltaic grid connection, a large number of photovoltaic grid connections bring about huge uncertainty to the power distribution network, so that safety risks such as voltage out-of-limit, aggravated voltage unbalance, line overload and the like are generated. In addition, with the popularization of electric vehicles, electrification of a traffic system will also have a significant influence on a power distribution network. Unlike traditional residential loads, the rapid increase in charging load of electric vehicles presents a significant challenge for safe operation of the distribution network. The uncertainty of the charging behavior of the electric automobile increases unpredictable operation risks of the power grid, and further worsens the safety of the power distribution network. In particular, public charging stations are often built integrally with renewable energy power generation systems, such as solar panels integrated on roofs, which makes the interaction between the aggregate electric vehicle and the photovoltaic more complex.
Because the photovoltaic and electric vehicles are connected in a high proportion, the operation of the power distribution network has obvious random characteristics, and therefore, the probability calculation and analysis of the power distribution network are significant. In the face of potential risks from various uncertainties, it is necessary to provide economic guidance for flexible resource allocation to mitigate fluctuations in the operating state of the distribution network. However, photovoltaic and electric vehicles in the distribution network are numerous and have different characteristics, so that it is often not feasible to process all uncertain factors indiscriminately, and a serious calculation burden is caused, so that further quantitative analysis of uncertainty in the distribution network is necessary. One possible approach is to identify key random variables that affect the system security and then formulate a specific flexible resource allocation scheme to cope with these major uncertainties. Therefore, the running state of the power distribution network can be improved, and the utilization efficiency of the power distribution network assets can be improved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for identifying the key uncertain factors of the power distribution network of the photovoltaic and electric automobile with high proportion, which can identify the key uncertain factors.
The technical scheme adopted by the invention is as follows: a method for identifying key uncertain factors of a power distribution network of an electric automobile with high proportion of photovoltaic and electric automobiles comprises the following steps:
1) Inputting a deterministic parameter and a randomness parameter of the power distribution network according to the selected power distribution network; the deterministic parameters of the distribution network comprise a network topology connection relation, line resistance reactance, load rated power and installation positions, photovoltaic installation capacity and installation positions, and installation capacity and installation positions of charging loads of the electric automobile; the power distribution network randomness parameters comprise probability distribution and parameters of loads, probability distribution and parameters of illumination intensity, probability distribution and parameters of electric vehicle charging loads and correlation coefficients among random variables in a power distribution network probability space;
2) According to the randomness parameters of the power distribution network provided in the step 1), the load, the illumination intensity and the charging load of the electric automobile are used as random variables xi in the probability space of the power distribution network, mutually independent random variable samples in the standard normal space are obtained by adopting a quasi-Monte Carlo method, and the random variable samples in the probability space of the power distribution network are obtained by utilizing Nataf transformation;
3) Establishing a deterministic power flow calculation model of the power distribution network according to the deterministic power flow parameters of the power distribution network provided in the step 1), and calculating to obtain a power distribution network voltage risk index as a target response according to the random variable sample in the probability space of the power distribution network obtained in the step 2);
4) Establishing an index set of random variables in a probability space of the power distribution network according to the power distribution network randomness parameters provided in the step 1), and dividing a subset and a complement of the random variable indexes; selecting an orthogonal polynomial basis according to probability distribution of the load, the illumination intensity and the charging load of the electric vehicle in the step 1), establishing a low-rank approximation model of a power distribution network voltage risk index according to the random variable samples which are mutually independent in the standard normal space provided in the step 2) and the target response obtained in the step 3), and solving the low-rank approximation model by adopting a sequential correction-update method;
5) Generating mutually independent random variable samples in two groups of standard normal spaces by adopting a quasi-Monte Carlo method, and calculating the global sensitivity of each non-empty subset of random variables in the probability space of the power distribution network by adopting a global sensitivity analysis method based on the mutually independent random variable samples in the two groups of standard normal spaces and the low-rank approximation model of the power distribution network voltage risk index obtained in the step 4);
6) And sequencing the global sensitivity of each non-empty subset of the random variables in the probability space of the power distribution network, and identifying key uncertain factors affecting the power distribution network voltage risk index.
The identification method for the key uncertain factors of the power distribution network containing the high-proportion photovoltaic and the electric automobile can comprehensively consider the random characteristics of the high-proportion photovoltaic and the electric automobile in the power distribution network, and establish the mapping relation between the original probability space and the standard normal space of the power distribution network through the Nataff transformation. The sensitivity analysis of the random variables is carried out based on the low-rank approximation model, so that the calculation scale can be effectively reduced, and the calculation speed is increased. The importance of the random variable affecting the power distribution network voltage risk index is ordered according to the global sensitivity, key uncertain factors are identified, decision reference is provided for reactive capacity configuration of the photovoltaic inverter, and the safe operation of the power distribution network is effectively improved while the investment economy is improved.
Drawings
FIG. 1 is a frame diagram of a method for identifying key uncertainty factors of a power distribution network of an electric vehicle with high proportion of photovoltaic and electric vehicles;
FIG. 2 is a topology diagram of an improved IEEE 33 distribution network in an embodiment;
FIG. 3a is a probability density distribution of voltage magnitudes at nodes 18 of a power distribution network in an embodiment;
FIG. 3b is a cumulative distribution function of the voltage magnitude at the distribution network node 18 in an embodiment;
FIG. 4 is a graph of the convergence relationship between the global sensitivity of photovoltaic and the number of samples at the distribution network node 18 in an embodiment;
FIG. 5 is a global sensitivity of a random variable of a power distribution network in an embodiment;
FIG. 6 is a cumulative distribution function of voltage risk indicators before and after dimension reduction of a power distribution network in an embodiment;
fig. 7a is a system voltage distribution in the case of an embodiment in which the distribution network is not configured with reactive capacity of a photovoltaic converter;
Fig. 7b is a system voltage distribution of the power distribution network in the case of configuring the reactive capacity of the photovoltaic converter at the first 4 nodes with maximum global sensitivity in the embodiment;
FIG. 8a is a distribution network voltage risk indicator probability density distribution in an embodiment;
fig. 8b is a graph showing a cumulative distribution function of power distribution network voltage risk indicators in an embodiment.
Detailed Description
The method for identifying the key uncertain factors of the power distribution network containing the high-proportion photovoltaic and electric vehicles is described in detail below with reference to the embodiment and the attached drawings.
As shown in fig. 1, the method for identifying the key uncertain factors of the power distribution network of the electric automobile with high proportion of photovoltaic and comprises the following steps:
1) Inputting a deterministic parameter and a randomness parameter of the power distribution network according to the selected power distribution network; the deterministic parameters of the distribution network comprise a network topology connection relation, line resistance reactance, load rated power and installation positions, photovoltaic installation capacity and installation positions, and installation capacity and installation positions of charging loads of the electric automobile; the power distribution network randomness parameters comprise probability distribution and parameters of loads, probability distribution and parameters of illumination intensity, probability distribution and parameters of electric vehicle charging loads and correlation coefficients among random variables in a power distribution network probability space;
For the embodiment of the invention, the adopted power distribution network containing high proportion of photovoltaic and electric vehicles is shown in fig. 2, the voltage level, the topological structure, the branch parameters and the node load parameters of the power distribution network are consistent with those of an IEEE33 node standard calculation example, the voltage level is 12.66kV, and the total active power requirement and the total reactive power requirement of the load are 3.1750MW and 2.3000Mvar respectively. The detailed parameters are shown in tables 1 and 2. Node voltage deviation severity coefficient The weight coefficient alpha=0.4, beta=0.6 of the average value and the maximum value of the power distribution network voltage risk index. The photovoltaic access position and capacity of the distribution network are shown in table 3, the access position and capacity of the electric automobile are shown in table 4, and the probability distribution of random variables and parameters thereof are shown in table 5.
Table 1 IEEE33 node distribution network example load access location and power
Table 2 IEEE33 node Power distribution network example line parameters
Table 3 photovoltaic access locations and capacities
| Node | Capacity (kWp) | Node | Capacity (kWp) |
| 9 | 100 | 21 | 100 |
| 11 | 100 | 24 | 100 |
| 12 | 200 | 25 | 200 |
| 16 | 600 | 28 | 1000 |
| 17 | 600 | 32 | 100 |
| 18 | 800 | 33 | 500 |
Table 4 electric vehicle access location and capacity
| Node | Capacity (kW) | Node | Capacity (kW) |
| 5 | 200 | 24 | 100 |
| 10 | 200 | 27 | 200 |
| 16 | 600 | 29 | 800 |
| 22 | 100 | 30 | 800 |
Table 5 probability distribution of random variables and parameters for distribution network
2) According to the randomness parameters of the power distribution network provided in the step 1), the load, the illumination intensity and the charging load of the electric automobile are used as random variables xi in the probability space of the power distribution network, mutually independent random variable samples in the standard normal space are obtained by adopting a quasi-Monte Carlo method, and the random variable samples in the probability space of the power distribution network are obtained by utilizing Nataf transformation;
The method for obtaining the random variable sample in the probability space of the power distribution network by utilizing the Nataff transformation specifically comprises the following steps:
According to the correlation coefficient rho ij among random variables in the probability space of the power distribution network, solving a correlation coefficient matrix rho φ in a standard normal space:
in the method, in the process of the invention, Is the ith random variable in standard normal spaceIs a cumulative distribution function of (1); g i(ξi) is the cumulative distribution function of the ith random variable ζ i in the distribution grid probability space; is the ith random variable in standard normal space And the jth random variableI.e. the i-th row and j-th column elements of the correlation coefficient matrix ρ φ in standard normal space; ρ ij is the correlation coefficient of the ith random variable ζ i and the jth random variable ζ j in the power distribution network probability space; phi 2 is a probability density function of a 2-ary standard normal distribution; mu i and mu j are the expectations of an ith random variable zeta i and a jth random variable zeta j in the power distribution network probability space, respectively, and sigma i and sigma j are standard deviations of an ith random variable zeta i and a jth random variable zeta j in the power distribution network probability space, respectively;
Square root decomposition is carried out on a correlation coefficient matrix rho φ in a standard normal space, so that a random variable zeta= (zeta 1,ξ2,…,ξn) sample in a power distribution network probability space is obtained according to mutually independent random variable zeta samples in the standard normal space, and the method is as follows:
ρφ＝LLT (3)
Wherein L represents a lower triangular matrix, and ζ represents random variables independent of each other in a normal space of the standard.
3) Establishing a deterministic power flow calculation model of the power distribution network according to the deterministic power flow parameters of the power distribution network provided in the step 1), and calculating to obtain a power distribution network voltage risk index as a target response according to the random variable sample in the probability space of the power distribution network obtained in the step 2); wherein,
(1) The deterministic power flow calculation model of the power distribution network is expressed as follows:
in the method, in the process of the invention, Representing state variables of the power distribution network, including node voltage phase angle theta and amplitude U; ζ= [ P Load,PEV,τ]T ] represents a random variable in a probability space of the power distribution network, and the random variable comprises load active power P Load, electric vehicle charging load active power P EV and illumination intensity tau; p m is the injected active power of the node m in the power distribution network, Q m is the injected reactive power of the node m in the power distribution network, and θ mc is the voltage phase angle difference between the node m and the node c; u m and U c are voltage amplitudes of a node m and a node c respectively, and G mc and B mc are real parts and imaginary parts of an m-th row and a c-th column element of the node admittance matrix of the power distribution network respectively.AndRespectively representing active power and reactive power transmitted by a node m from a transformer substation; And Respectively representing the active power and the reactive power of the load of the node m; Represents the photovoltaic active power under the condition of the illumination intensity tau m at the node m, Representing the active power of the charging load of the electric automobile at the node m; n d represents the number of nodes of the power distribution network;
(2) The power distribution network voltage risk index adopts the following formula:
δ(Um)＝|Um-1| (9)
Where n is a power distribution network voltage risk indicator, delta (U m) is the voltage deviation of node m, Is a severity coefficient, S δ(Um) is a node m voltage deviation severity, and α and β are weight coefficients.
4) Establishing an index set of random variables in a probability space of the power distribution network according to the power distribution network randomness parameters provided in the step 1), and dividing a subset and a complement of the random variable indexes; selecting an orthogonal polynomial basis according to probability distribution of the load, the illumination intensity and the charging load of the electric vehicle in the step 1), establishing a low-rank approximation model of a power distribution network voltage risk index according to the random variable samples which are mutually independent in the standard normal space provided in the step 2) and the target response obtained in the step 3), and solving the low-rank approximation model by adopting a sequential correction-update method; wherein,
(1) The method for establishing the index set of the random variable in the probability space of the power distribution network and dividing the subset and the complement of the random variable index specifically comprises the following steps:
ζ= (ζ 1,ξ2,…,ξn) is a random variable in the power distribution network probability space, and the index set of the random variable in the power distribution network probability space is Δ= {1,2, …, n }, n is the total number of the random variables; setting a random variable index subset k= { i 1,…,is } ∈delta, wherein s is more than or equal to 1 and less than or equal to n, and ζ k is a non-empty subset with the ζ index subset k, and a random variable index complement set
(2) The low-rank approximation model of the power distribution network voltage risk index is expressed as:
where h is a power distribution network voltage risk indicator, Is the low rank approximation estimation of the power distribution network voltage risk index, b l is the normalized weight factor when the rank is l, ω l (ζ) is the rank-one function of the random variable ζ in the power distribution network probability space when the rank is l,The method is a single variable function of an ith random variable xi i in a power distribution network probability space when the rank is l, and r is the maximum development rank of low-rank approximation estimation;
Will be On a polynomial basis orthogonal to the corresponding probability distributionThe low-rank approximation model of the power distribution network voltage risk index is further expressed as:
in the method, in the process of the invention, Is the q-th order polynomial of the i-th random variable xi i in the probability space of the distribution network,The method is a q-th order polynomial coefficient of an ith random variable xi i in a power distribution network probability space when the rank is l, and gamma is the maximum expansion order of the polynomial;
(3) The method for solving the low-rank approximation model by adopting the sequential correction-update method comprises the following steps:
(3.1) considering an experimental design with a random variable sample size of N, wherein the experimental design comprises a random variable sample xi N＝(ξ(1),…,ξ(N)) and a power distribution network voltage risk index sample h N＝(h(1),…,h(N)); giving a low-rank approximation estimation maximum expansion rank r and a polynomial maximum expansion rank gamma, setting the maximum iteration number as I max, and setting the maximum relative iteration error as e max; initializing a rank number l=1;
(3.2) judging whether the current rank number l=l+1 is larger than a given low rank approximation estimated maximum expansion rank number r, if yes, ending, and if not, entering a step (3.3);
(3.3) initializing iteration number I l =0, initializing relative iteration error
(3.4) Determining relative iteration errorIf the iteration error is smaller than the set maximum iteration error, the iteration error is e max, or if the iteration number I l is larger than the set maximum iteration number I max, the step (3.9) is carried out if the iteration error is satisfied, and if the iteration error is not satisfied, the step (3.5) is carried out;
(3.5) iteration number I l＝Il +1;
(3.6) solving the minimization problem described by the formula (18) by converting the formula (17) of the rank-one function omega l (ζ) of the ith random variable xi i (i=1, …, n) in the probability space of the power distribution network into the minimization problem described by the formula (18) by adopting an alternating least square method to solve the following problem of the rank-one function of the random variable xi in the probability space of the power distribution network when the rank is l, thereby obtaining the polynomial coefficient of the ith random variable xi i in the probability space of the power distribution network when the rank is l Then update with (19)
In the method, in the process of the invention,Representing the residual error of the power distribution network voltage risk index h when the rank is (l-1), h (t) represents the t power distribution network voltage risk index sample,Representing low-rank approximation estimation of a power distribution network voltage risk index on a t-th random variable sample xi (t) when the rank is (l-1); w represents a rank vector space, ω being an optimizing variable in W; r γ represents a gamma-order polynomial coefficient space, kappa q is an optimizing variable in R γ, and kappa is an optimizing variable set in R γ;
And (3.7) solving by using the formula (20) to obtain a rank-one function omega l (xi) of a random variable xi in a probability space of the power distribution network when the rank is l:
(3.8) calculating the relative iteration error using equation (21) Then go to step (3.4):
in the method, in the process of the invention, Representing the relative error of the iteration,Representing a variance calculation;
(3.9) solving equation (22) describing the minimization problem, resulting in a normalized set of weight factors b= { b 1,…,bl }:
Wherein R l represents a normalized weight factor space when the rank is l, ψ l is an optimizing variable in R l, and ψ is an optimizing variable set in R l;
(3.10) calculating a low rank approximation of the power distribution network voltage risk indicator using the following equation (23), and then proceeding to step (3.2):
in the method, in the process of the invention, Is low-rank approximation estimation of a power distribution network voltage risk index when the rank is l, b π is a normalized weight factor when the rank is pi, and omega π (xi) is a rank-one function of a random variable xi in a power distribution network probability space when the rank is pi.
The uncertainty conductivity of the low-rank approximation model is illustrated by taking the voltage assignment of the power distribution network node 18 in the embodiment as an example, in the embodiment, probability density distribution and cumulative distribution functions of the voltage amplitude of the power distribution network node 18 are respectively shown in fig. 3a and fig. 3b, it can be seen that the low-rank approximation model and the monte carlo method have similar results, and the probability of the voltage out-of-limit of the node 18 exceeds 30%.
5) Generating mutually independent random variable samples in two groups of standard normal spaces by adopting a quasi-Monte Carlo method, and calculating the global sensitivity of each non-empty subset of random variables in the probability space of the power distribution network by adopting a global sensitivity analysis method based on the mutually independent random variable samples in the two groups of standard normal spaces and the low-rank approximation model of the power distribution network voltage risk index obtained in the step 4); comprising the following steps:
the expression form of the power distribution network voltage risk index based on variance decomposition is obtained by adopting the following steps:
Wherein, h (ζ) is a power distribution network voltage risk index considering the influence of a random variable ζ in a power distribution network probability space, and h 0 represents the expectation of h (ζ); k and v represent index subsets of random variable ζ in the probability space of the power distribution network, ζ k and ζ v are non-empty subsets of random variable ζ in the probability space of the power distribution network, h k(ξk) and h v(ξv) represent power distribution network voltage risk indicators considering the influence of ζ k and ζ v, respectively; Representing a desired operation.
The variance D of h (ζ), expressed as:
Where D represents the variance of h (ζ), D k represents the variance of a non-null subset ζ k of the random variable ζ in the probability space of the distribution network, Representing a variance calculation;
The global sensitivity of the non-null subset xi k of the random variable xi in the probability space of the power distribution network is calculated by adopting the following formula:
Where S k represents the interaction influencing factor of the non-null subset ζ k of the random variable ζ in the probability space of the distribution network, The global sensitivity of the non-null subset ζ k representing the random variable ζ in the power distribution network probability space;
Order the Wherein the method comprises the steps ofIndicating the expected value of h (ζ) when ζ k is taken as a condition. Due to So the global sensitivity of the non-null subset xi k of the random variable xi in the probability space of the distribution networkFurther expressed as:
Two cases that each component in random variable xi in the probability space of the power distribution network is independent and has correlation are discussed respectively:
(1) When all components in random variable xi in the probability space of the power distribution network are mutually independent, the global sensitivity of a non-null subset xi k of the random variable xi in the probability space of the power distribution network based on low-rank approximation model The formula of (2) is as follows:
In the middle of Representing the global sensitivity of a non-null subset ζ k of random variables ζ in the probability space of the distribution network based on a low-rank approximation model, h LRA (ζ) representing a distribution network voltage risk indicator based on a low-rank approximation model that considers the influence of random variables ζ in the probability space of the distribution network,Represents the expected value of h LRA (ζ) when ζ k is taken as a condition;
the relationship is calculated from the orthogonality of the probability distribution corresponding polynomials by:
Obtaining In the calculationAndThe analytical formula of (c) is represented as follows:
Where xi i and xi j are the ith and jth random variables in the probability space of the distribution network, AndThe method is a single variable function of an ith random variable xi i in a power distribution network probability space when the rank is l and the rank is m; is the 0 th order polynomial coefficient of the i-th random variable xi i in the probability space of the distribution network when the rank is l, AndThe k-th order polynomial coefficients of the i-th random variable xi i in the distribution network probability space when the rank is l and the rank is m respectively,AndThe q-th order polynomial coefficients of the i-th random variable xi i in the power distribution network probability space when the rank is l and the rank is m respectively; b l and b m are normalized weighting factors for rank l and rank m, respectively; r is the maximum expansion rank number of low rank approximation estimation, n is the total number of random variables, and gamma is the maximum expansion rank number of polynomials;
(2) When the correlation exists among all components in random variable xi in the probability space of the power distribution network, the global sensitivity of a non-null subset xi k of the random variable xi in the probability space of the power distribution network based on the Monte Carlo method The formula of (2) is as follows:
Wherein, the random variables ζ= (ζ k,ξw),ξk and ζ w are two complementary subsets of ζ) in the power distribution network probability space; And Respectively representing conditional probability distributions from probability spaces of distribution networksTwo different random variable subsets obtained by middle sampling; Representing and considering random variables in probability space of power distribution network An affected power distribution network voltage risk indicator;
therefore, the global sensitivity of the non-null subset ζ k of the random variable ζ in the power distribution network probability space based on the low-rank approximation model The calculation formula of (2) is as follows:
wherein ζ represents a random variable in a standard normal space in which ζ is obtained by Natav conversion, ζ k represents a random variable in a standard normal space in which ζ k is obtained by Natav conversion, and ζ' w represents Random variables in a standard normal space obtained by the natto transform.
Taking photovoltaic at the distribution network node 18 as an example in the embodiment, the accuracy and the solving efficiency of the global sensitivity are solved based on a low-rank approximation model. In the embodiment, the convergence relationship between the global sensitivity and the sampling number of the photovoltaic at the power distribution network node 18 is shown in fig. 4, it can be seen that the convergence can be stabilized based on the low-rank approximation model method, and the convergence accuracy is similar to that of the monte carlo method. The global sensitivity calculation efficiency pair of the photovoltaic at the node 18 is shown in a table 6, so that the low-rank approximation model has higher solving efficiency than the Monte Carlo method, and has advantages in the aspects of model construction and evaluation solving compared with a polynomial chaotic expansion method. The global sensitivity of the random variables of the distribution network in an embodiment is shown in fig. 5.
Table 6 global sensitivity calculation efficiency vs. photovoltaic at node 18
6) And sequencing the global sensitivity of each non-empty subset of the random variables in the probability space of the power distribution network, and identifying key uncertain factors affecting the power distribution network voltage risk index.
For embodiments of the present invention, the converter reactive capacity is configured with a power factor of 0.9 and the output strategy is controlled using an in-situ voltage-reactive curve with limits of 0.95 and 1.08p.u.
In order to verify the feasibility and effectiveness of the identification method containing the high-proportion photovoltaic and electric automobile distribution network key uncertain factors, in the embodiment, the following 5 scenes are adopted for verification analysis:
scene I: the original scene is considered, 52-dimensional random variables are considered, and the photovoltaic reactive capacity is not configured;
scene II: taking a threshold value of 0.015, and only considering a 14-dimensional random variable with global sensitivity larger than the threshold value;
Scene III: the reactive capacity of the converter is configured only at the photovoltaic with the highest global sensitivity;
Scene IV: the reactive capacity of the converter is configured at the first 4 photovoltaic configuration converters with the highest global sensitivity;
Scene V: inverter reactive capacity is configured at all photovoltaics.
In the embodiment, the cumulative distribution function of the voltage risk indexes before and after the dimension reduction of the power distribution network is shown in fig. 6, the situation that only random variables with larger global sensitivity are reserved, and random variables with small global sensitivity are treated as deterministic variables can be seen, so that the system uncertainty is reduced while the solving precision is ensured.
In the embodiment, the system voltage distribution under the condition that the power distribution network is not provided with the reactive capacity of the photovoltaic converter and the system voltage distribution under the condition that the reactive capacity of the photovoltaic converter is provided at the first 4 nodes with the maximum global sensitivity are respectively shown in fig. 7a and 7b, so that the system voltage distribution is obviously improved by the configuration of the reactive capacity of the photovoltaic converter at the first 4 nodes with the maximum global sensitivity.
In the embodiment, the probability density distribution and the cumulative distribution function of the power distribution network voltage risk indicator are respectively shown in fig. 8a and 8b, so that the effect of reducing the power distribution network voltage risk indicator by the reactive capacity of the first 4 photovoltaic configuration converters with the maximum global sensitivity is similar to the effect of reducing the reactive capacity of all photovoltaic configuration converters, and the investment is less, and the provided identification method containing the key uncertain factors of the power distribution network of the high-proportion photovoltaic and electric vehicles can provide guidance for the configuration of the reactive capacity of the photovoltaic converters.
Claims (4)
1. The method for identifying the key uncertain factors of the distribution network of the electric automobile with high proportion of photovoltaic and electric automobiles is characterized by comprising the following steps:
1) Inputting a deterministic parameter and a randomness parameter of the power distribution network according to the selected power distribution network; the deterministic parameters of the distribution network comprise a network topology connection relation, line resistance reactance, load rated power and installation positions, photovoltaic installation capacity and installation positions, and installation capacity and installation positions of charging loads of the electric automobile; the power distribution network randomness parameters comprise probability distribution and parameters of loads, probability distribution and parameters of illumination intensity, probability distribution and parameters of electric vehicle charging loads and correlation coefficients among random variables in a power distribution network probability space;
2) According to the randomness parameters of the power distribution network provided in the step 1), the load, the illumination intensity and the charging load of the electric automobile are used as random variables xi in the probability space of the power distribution network, mutually independent random variable samples in the standard normal space are obtained by adopting a quasi-Monte Carlo method, and the random variable samples in the probability space of the power distribution network are obtained by utilizing Nataf transformation;
3) Establishing a deterministic power flow calculation model of the power distribution network according to the deterministic power flow parameters of the power distribution network provided in the step 1), and calculating to obtain a power distribution network voltage risk index as a target response according to the random variable sample in the probability space of the power distribution network obtained in the step 2);
4) Establishing an index set of random variables in a probability space of the power distribution network according to the power distribution network randomness parameters provided in the step 1), and dividing a subset and a complement of the random variable indexes; selecting an orthogonal polynomial basis according to probability distribution of the load, the illumination intensity and the charging load of the electric vehicle in the step 1), establishing a low-rank approximation model of a power distribution network voltage risk index according to the random variable samples which are mutually independent in the standard normal space provided in the step 2) and the target response obtained in the step 3), and solving the low-rank approximation model by adopting a sequential correction-update method;
5) Generating mutually independent random variable samples in two groups of standard normal spaces by adopting a quasi-Monte Carlo method, and calculating the global sensitivity of each non-empty subset of random variables in the probability space of the power distribution network by adopting a global sensitivity analysis method based on the mutually independent random variable samples in the two groups of standard normal spaces and the low-rank approximation model of the power distribution network voltage risk index obtained in the step 4); comprising the following steps:
the expression form of the power distribution network voltage risk index based on variance decomposition is obtained by adopting the following steps:
Wherein, h (ζ) is a power distribution network voltage risk index considering the influence of a random variable ζ in a power distribution network probability space, and h 0 represents the expectation of h (ζ); k and v represent index subsets of random variable ζ in the probability space of the power distribution network, ζ k and ζ v are non-empty subsets of random variable ζ in the probability space of the power distribution network, h k(ξk) and h v(ξv) represent power distribution network voltage risk indicators considering the influence of ζ k and ζ v, respectively; Representing a desired operation;
The variance D of h (ζ), expressed as:
Where D represents the variance of h (ζ), D k represents the variance of a non-null subset ζ k of the random variable ζ in the probability space of the distribution network, Representing a variance calculation;
The global sensitivity of the non-null subset xi k of the random variable xi in the probability space of the power distribution network is calculated by adopting the following formula:
Where S k represents the interaction influencing factor of the non-null subset ζ k of the random variable ζ in the probability space of the distribution network, The global sensitivity of the non-null subset ζ k representing the random variable ζ in the power distribution network probability space;
Order the Wherein the method comprises the steps ofRepresents the expected value of h (ζ) when ζ k is taken as a condition; due to So the global sensitivity of the non-null subset xi k of the random variable xi in the probability space of the distribution networkFurther expressed as:
Two cases that each component in random variable xi in the probability space of the power distribution network is independent and has correlation are discussed respectively:
(1) When all components in random variable xi in the probability space of the power distribution network are mutually independent, the global sensitivity of a non-null subset xi k of the random variable xi in the probability space of the power distribution network based on low-rank approximation model The formula of (2) is as follows:
In the middle of Representing the global sensitivity of a non-null subset ζ k of random variables ζ in the probability space of the distribution network based on a low-rank approximation model, h LRA (ζ) representing a distribution network voltage risk indicator based on a low-rank approximation model that considers the influence of random variables ζ in the probability space of the distribution network,Represents the expected value of h LRA (ζ) when ζ k is taken as a condition;
the relationship is calculated from the orthogonality of the probability distribution corresponding polynomials by:
Obtaining In the calculationAndThe analytical formula of (c) is represented as follows:
Where xi i and xi j are the ith and jth random variables in the probability space of the distribution network, AndThe single variable function is the ith random variable xi i in the probability space of the distribution network when the rank is l and the rank is m respectively; is the 0 th order polynomial coefficient of the i-th random variable xi i in the probability space of the distribution network when the rank is l, AndThe k-th order polynomial coefficients of the i-th random variable xi i in the distribution network probability space when the rank is l and the rank is m respectively,AndThe q-th order polynomial coefficients of the i-th random variable xi i in the power distribution network probability space when the rank is l and the rank is m respectively; b l and b m are normalized weighting factors for rank l and rank m, respectively; r is the maximum expansion rank number of low rank approximation estimation, n is the total number of random variables, and gamma is the maximum expansion rank number of polynomials;
(2) When the correlation exists among all components in random variable xi in the probability space of the power distribution network, the global sensitivity of a non-null subset xi k of the random variable xi in the probability space of the power distribution network based on the Monte Carlo method The formula of (2) is as follows:
Wherein, the random variables ζ= (ζ k,ξw),ξk and ζ w are two complementary subsets of ζ) in the power distribution network probability space; And Respectively representing conditional probability distributions from probability spaces of distribution networksTwo different random variable subsets obtained by middle sampling; Representing and considering random variables in probability space of power distribution network An affected power distribution network voltage risk indicator;
therefore, the global sensitivity of the non-null subset ζ k of the random variable ζ in the power distribution network probability space based on the low-rank approximation model The calculation formula of (2) is as follows:
Wherein ζ represents a random variable in a standard normal space obtained by zeta-Natav transformation, ζ k represents a random variable in a standard normal space obtained by zeta- k by Natav transformation, and ζ' w represents Random variables in a standard normal space obtained through Nataff transformation;
6) And sequencing the global sensitivity of each non-empty subset of the random variables in the probability space of the power distribution network, and identifying key uncertain factors affecting the power distribution network voltage risk index.
2. The method for identifying the key uncertainty factors of the distribution network containing the high-proportion photovoltaic and the electric automobile according to claim 1 is characterized in that the method for identifying the key uncertainty factors of the distribution network containing the high-proportion photovoltaic and the electric automobile according to step 2) is characterized by comprising the following steps of:
According to the correlation coefficient rho ij among random variables in the probability space of the power distribution network, solving a correlation coefficient matrix rho φ in a standard normal space:
in the method, in the process of the invention, Is the ith random variable in standard normal spaceIs a cumulative distribution function of (1); g i(ξi) is the cumulative distribution function of the ith random variable ζ i in the distribution grid probability space; is the ith random variable in standard normal space And the jth random variableI.e. the i-th row and j-th column elements of the correlation coefficient matrix ρ φ in standard normal space; ρ ij is the correlation coefficient of the ith random variable ζ i and the jth random variable ζ j in the power distribution network probability space; phi 2 is a probability density function of a 2-ary standard normal distribution; mu i and mu j are the expectations of an ith random variable zeta i and a jth random variable zeta j in the power distribution network probability space, respectively, and sigma i and sigma j are standard deviations of an ith random variable zeta i and a jth random variable zeta j in the power distribution network probability space, respectively;
Square root decomposition is carried out on a correlation coefficient matrix rho φ in a standard normal space, so that a random variable zeta= (zeta 1,ξ2,…,ξn) sample in a power distribution network probability space is obtained according to mutually independent random variable zeta samples in the standard normal space, and the method is as follows:
ρφ＝LLT (3)
Wherein L represents a lower triangular matrix, and ζ represents random variables independent of each other in a normal space of the standard.
3. The identification method of the key uncertainty factors of the distribution network containing the high-proportion photovoltaic and the electric automobile according to claim 1, wherein the deterministic power flow calculation model of the distribution network in the step 3) is represented as follows:
in the method, in the process of the invention, Representing state variables of the power distribution network, including node voltage phase angle theta and amplitude U; ζ= [ P Load,PEV,τ]T ] represents a random variable in a probability space of the power distribution network, and the random variable comprises load active power P Load, electric vehicle charging load active power P EV and illumination intensity tau; p m is the injected active power of the node m in the power distribution network, Q m is the injected reactive power of the node m in the power distribution network, and θ mc is the voltage phase angle difference between the node m and the node c; u m and U c are voltage amplitudes of a node m and a node c respectively, and G mc and B mc are real parts and imaginary parts of an m-th row and a c-th column element of a node admittance matrix of the power distribution network respectively; And Respectively representing active power and reactive power transmitted by a node m from a transformer substation; And Respectively representing the active power and the reactive power of the load of the node m; Represents the photovoltaic active power under the condition of the illumination intensity tau m at the node m, Representing the active power of the charging load of the electric automobile at the node m; n d represents the number of nodes of the power distribution network;
The power distribution network voltage risk index adopts the following formula:
δ(Um)＝|Um-1| (9)
Where h is a power distribution network voltage risk indicator, delta (U m) is the voltage deviation of node m, Is a severity coefficient, S δ(Um) is a node m voltage deviation severity, and α and β are weight coefficients.
4. The method for identifying the key uncertainty factors of the distribution network containing the high-proportion photovoltaic and the electric automobile according to claim 1, wherein the establishing the index set of the random variable in the probability space of the distribution network in the step 4) and dividing the subset and the complement of the random variable index specifically comprises the following steps:
ζ= (ζ 1,ξ2,…,ξn) is a random variable in the power distribution network probability space, and the index set of the random variable in the power distribution network probability space is Δ= {1,2, …, n }, n is the total number of the random variables; setting a random variable index subset k= { i 1,…,is } ∈delta, wherein s is more than or equal to 1 and less than or equal to n, and ζ k is a non-empty subset with the ζ index subset k, and a random variable index complement set
The low-rank approximation model of the power distribution network voltage risk index is expressed as:
where h is a power distribution network voltage risk indicator, Is the low rank approximation estimation of the power distribution network voltage risk index, b l is the normalized weight factor when the rank is l, ω l (ζ) is the rank-one function of the random variable ζ in the power distribution network probability space when the rank is l,The method is a single variable function of an ith random variable xi i in a power distribution network probability space when the rank is l, and r is the maximum development rank of low-rank approximation estimation;
Will be On a polynomial basis orthogonal to the corresponding probability distributionThe low-rank approximation model of the power distribution network voltage risk index is further expressed as:
in the method, in the process of the invention, Is the q-th order polynomial of the i-th random variable xi i in the probability space of the distribution network,The method is a q-th order polynomial coefficient of an ith random variable xi i in a power distribution network probability space when the rank is l, and gamma is the maximum expansion order of the polynomial;
the method for solving the low-rank approximation model by adopting the sequential correction-update method comprises the following steps:
(1) Considering an experimental design with a random variable sample size of N, wherein the experimental design comprises a random variable sample xi N＝(ξ(1),…,ξ(N)) and a power distribution network voltage risk index sample h N＝(h(1),…,h(N)); giving a low-rank approximation estimation maximum expansion rank r and a polynomial maximum expansion rank gamma, setting the maximum iteration number as I max, and setting the maximum relative iteration error as e max; initializing a rank number l=1;
(2) Judging whether the current rank number l=l+1 is larger than a given low rank approximation estimated maximum expansion rank number r, if yes, ending, and if not, entering a step (3);
(3) Initializing iteration number I l =0, and initializing relative iteration error
(4) Judging relative iteration errorIf the iteration error is smaller than the set maximum iteration error, the iteration error is e max, or if the iteration number I l is larger than the set maximum iteration number I max, the step (9) is carried out if the iteration error is satisfied, and the step (5) is carried out if the iteration error is not satisfied;
(5) Iteration number I l＝Il +1;
(6) Solving a minimization problem described by a formula (18) by converting a formula (17) of a rank-one function omega l (xi) of the ith random variable xi i, i=1, … and n in a power distribution network probability space into a formula (18) by adopting an alternating least square method to obtain a polynomial coefficient of the ith random variable xi i in the power distribution network probability space when the rank is l Then update with (19)
In the method, in the process of the invention,Representing the residual error of the power distribution network voltage risk index h when the rank is (l-1), h (t) represents the t power distribution network voltage risk index sample,Representing low-rank approximation estimation of a power distribution network voltage risk index on a t-th random variable sample xi (t) when the rank is (l-1); w represents a rank vector space, ω being an optimizing variable in W; r γ represents a gamma-order polynomial coefficient space, kappa q is an optimizing variable in R γ, and kappa is an optimizing variable set in R γ;
(7) Solving by using the formula (20) to obtain a rank-function omega l (xi) of a random variable xi in a power distribution network probability space when the rank is l:
(8) Calculating relative iteration errors using (21) Then enter the step (4):
in the method, in the process of the invention, Representing the relative error of the iteration,Representing a variance calculation;
(9) Solving equation (22) describing the minimization problem, resulting in a normalized set of weight factors b= { b 1,…,bl }:
Wherein R l represents a normalized weight factor space when the rank is l, ψ l is an optimizing variable in R l, and ψ is an optimizing variable set in R l;
(10) Calculating a low rank approximation estimate of the power distribution network voltage risk indicator using the following equation (23), and then entering step (2):
in the method, in the process of the invention, Is low-rank approximation estimation of a power distribution network voltage risk index when the rank is l, b π is a normalized weight factor when the rank is pi, and omega π (xi) is a rank-one function of a random variable xi in a power distribution network probability space when the rank is pi.
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