CN114897414A - Method for identifying key uncertain factors of power distribution network containing high-proportion photovoltaic and electric automobile - Google Patents
Method for identifying 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 containing high-proportion photovoltaic and electric vehicles comprises the following steps: inputting a power distribution network deterministic parameter and a power distribution network randomness parameter according to the selected power distribution network; obtaining mutually independent random variable samples in a standard normal space, and solving the random variable samples in a probability space of the power distribution network; establishing a deterministic load flow calculation model of the power distribution network to obtain a voltage risk index of the power distribution network 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 complementary set of random variable indexes; establishing and solving a low-rank approximation model of the voltage risk index of the power distribution network; 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 according to the obtained low-rank approximation model of the voltage risk index of the power distribution network; and identifying key uncertain factors influencing the voltage risk indexes of the power distribution network. The invention effectively improves the safe operation of the power distribution network while improving the investment economy.
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 containing high-proportion 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 consumption. However, after a large number of photovoltaic grids are connected, a great amount of uncertainty is brought to the distribution network, and thus safety risks such as voltage out-of-limit, increased voltage unbalance, line overload and the like are caused. In addition, with the popularization of electric vehicles, electrification of a traffic system will have a great influence on a power distribution network. Unlike traditional residential loads, the rapid increase in electric vehicle charging load presents a significant challenge to the safe operation of the distribution grid. The uncertainty of the charging behavior of the electric vehicle increases the unpredictable operation risk of the power grid, further deteriorating the safety of the power distribution network. In particular, public charging stations are often built integrated with renewable energy power generation systems, such as roof-top integrated solar panels, which further complicate the interaction between the polymer electric vehicle and the photovoltaic.
Due to the fact that photovoltaic and electric automobiles are connected in a high proportion, the operation of the power distribution network has an obvious random characteristic, and therefore the power distribution network probability calculation analysis is of great significance. 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 conditions of the distribution grid. However, the number of photovoltaic and electric vehicle accesses in the distribution network is large and different in characteristics, so that it is often not feasible to treat all uncertain factors without distinction, and a serious calculation burden is also caused, so that further quantitative analysis must be performed on the uncertainties in the distribution network. One possible approach is to identify key random variables that affect system security and then develop specific flexible resource allocation schemes to cope with these major uncertainties. Therefore, the running state of the power distribution network can be improved, and the utilization efficiency of the assets of the power distribution network can be improved.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for identifying key uncertain factors of a power distribution network of a high-proportion photovoltaic and electric vehicle, which can identify the key uncertain factors, in order to overcome the defects of the prior art.
The technical scheme adopted by the invention is as follows: a method for identifying key uncertain factors of a power distribution network containing high-proportion photovoltaic and electric vehicles comprises the following steps:
1) inputting a power distribution network deterministic parameter and a power distribution network randomness parameter according to the selected power distribution network; the power distribution network certainty parameters comprise a network topology connection relation, a line resistance reactance, a load rated power and an installation position, a photovoltaic installation capacity and an installation position, and an installation capacity and an installation position of an electric automobile charging load; the randomness parameters of the power distribution network 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 probability space of the power distribution network;
2) according to the power distribution network randomness parameters provided in the step 1), loads, illumination intensity and electric vehicle charging loads are used as random variables xi in a power distribution network probability space, a quasi-Monte Carlo method is adopted to obtain mutually independent random variable samples in a standard normal space, and Naphv transformation is utilized to obtain the random variable samples in the power distribution network probability space;
3) establishing a power distribution network deterministic load flow calculation model according to the power distribution network deterministic parameters 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 power distribution network probability space 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 randomness parameters of the power distribution network provided in the step 1), and dividing a subset and a complementary set of random variable indexes; selecting an orthogonal polynomial base according to the probability distribution of the load, the illumination intensity and the charging load of the electric automobile in the step 1), establishing a low-rank approximation model of the voltage risk index of the power distribution network according to mutually independent random variable samples 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, 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 voltage risk index of the power distribution network 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 influencing the voltage risk indexes of the power distribution network.
The method for identifying 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 Naphv transformation. Sensitivity analysis of random variables is carried out based on a low-rank approximation model, so that the calculation scale can be effectively reduced, and the calculation speed is accelerated. The importance of the random variable influencing the voltage risk index of the power distribution network is sequenced according to the global sensitivity, key uncertain factors are identified, decision reference is provided for the 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 uncertain factors of a power distribution network containing high-proportion photovoltaic power and electric vehicles according to the invention;
FIG. 2 is a diagram of an improved IEEE33 power distribution network topology of an embodiment;
FIG. 3a is a probability density distribution of voltage amplitudes of distribution network nodes 18 in an embodiment;
FIG. 3b is a cumulative distribution function of voltage amplitudes of distribution network nodes 18 in an embodiment;
FIG. 4 is a convergence relationship between the global sensitivity of the photovoltaic at the distribution network node 18 and the number of samples in an embodiment;
FIG. 5 is the global sensitivity of the random variables of the distribution network in the embodiment;
FIG. 6 is a cumulative distribution function of voltage risk indicators before and after dimensionality reduction of the distribution network in the embodiment;
FIG. 7a is a system voltage distribution of the power distribution network without photovoltaic converter reactive capacity configuration in the embodiment;
FIG. 7b is a system voltage distribution of the power distribution network in the embodiment under the condition that the reactive capacity of the photovoltaic converter is configured at the first 4 nodes with the maximum global sensitivity;
FIG. 8a is a distribution network voltage risk indicator probability density distribution in an embodiment;
fig. 8b is a cumulative distribution function of the distribution network voltage risk indicators in the embodiment.
Detailed Description
The method for identifying the key uncertain factors of the distribution network containing the high-proportion photovoltaic and electric vehicles is described in detail below by combining the embodiment and the attached drawings.
As shown in FIG. 1, the method for identifying the key uncertain factors of the distribution network containing the high-proportion photovoltaic power and the electric automobile comprises the following steps:
1) inputting a power distribution network deterministic parameter and a power distribution network randomness parameter according to the selected power distribution network; the power distribution network certainty parameters comprise a network topology connection relation, a line resistance reactance, a load rated power and an installation position, a photovoltaic installation capacity and an installation position, and an installation capacity and an installation position of an electric automobile charging load; the randomness parameters of the power distribution network 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 probability space of the power distribution network;
for the embodiment of the invention, the adopted power distribution network containing high-proportion photovoltaic and electric automobilesAs shown in fig. 2, the voltage class, the topology, the branch parameters and the node load parameters of the distribution network are consistent with the IEEE33 node standard calculation example, the voltage class is 12.66kV, and the total active power demand and the total reactive power demand 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 of the average value and the maximum value of the voltage risk index of the power distribution network is 0.4, and beta is 0.6. Distribution network photovoltaic access position and capacity are shown in table 3, electric vehicle access position and capacity are shown in table 4, and probability distribution of random variables and parameters thereof are shown in table 5.
TABLE 1 IEEE33 nodal point distribution network example load access position and power
TABLE 2 IEEE33 node distribution network example line parameters
TABLE 3 photovoltaic Access location and Capacity
| Node point | Capacity (kWp) | Node point | 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 point | Capacity (kW) | Node point | 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 of distribution network and its parameters
2) According to the power distribution network randomness parameters provided in the step 1), loads, illumination intensity and electric vehicle charging loads are used as random variables xi in a power distribution network probability space, a quasi-Monte Carlo method is adopted to obtain mutually independent random variable samples in a standard normal space, and Naphv transformation is utilized to obtain the random variable samples in the power distribution network probability space;
the method for obtaining the random variable sample in the probability space of the power distribution network by utilizing the Naphv transform specifically comprises the following steps:
according to the correlation coefficient rho between random variables in the probability space of the power distribution network ij Solving the correlation coefficient matrix rho in the standard normal space φ ：
In the formula (I), the compound is shown in the specification,
is the ith random variable in the standard normal space
The cumulative distribution function of; g i (ξ i ) Is the ith random variable xi in the probability space of the distribution network i The cumulative distribution function of;
is the ith random variable in the standard normal space
And jth random variable
The correlation coefficient of (1), i.e. the matrix of correlation coefficients p in the normal space φ Row i and column j elements of (1); rho ij Is the ith random variable xi in the probability space of the distribution network i And j-th random variable ξ j The correlation coefficient of (a); phi is a 2 Probability density function of 2-element standard normal distribution；μ i And mu j Respectively is the ith random variable xi in the probability space of the distribution network i And j-th random variable ξ j Expectation of (a) i And σ j Respectively is the ith random variable xi in the probability space of the distribution network i And j-th random variable ξ j Standard deviation of (d);
relating the matrix rho of the relation number in the standard normal space φ Performing square root decomposition, and obtaining a random variable xi (xi) in the probability space of the power distribution network according to independent random variable zeta samples in the standard normal space 1 ,ξ 2 ,…,ξ n ) Samples, as follows:
ρ φ ＝LL T (3)
in the formula, L represents a lower triangular matrix, and ζ represents mutually independent random variables in a standard normal space.
3) Establishing a power distribution network deterministic load flow calculation model according to the power distribution network deterministic parameters 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 power distribution network probability space obtained in the step 2); wherein the content of the first and second substances,
(1) the power distribution network deterministic load flow calculation model is represented as follows:
in the formula (I), the compound is shown in the specification,
representing state variables of the power distribution network, including a node voltage phase angle theta and an amplitude value U; xi ═ P Load ,P EV ,τ] T Representing random variables in the probability space of the distribution network, including the load active power P Load Active power P of charging load of electric automobile EV And the illumination intensity τ; p m Injecting active power, Q, for node m in a power distribution network m Injecting reactive power, theta, for node m in a distribution network mc Is the voltage phase angle difference of node m and node c; u shape m And U c Voltage amplitudes, G, of nodes m and c, respectively mc And B mc The real part and the imaginary part of the mth row and the mth column of the element of the power distribution network node admittance matrix are respectively.
And
respectively representing active power and reactive power transmitted by the transformer substation at a node m;
and
respectively representing the active power and the reactive power of the node m load;
representing the intensity of illumination tau at node m m The active power of the photovoltaic under the condition,
representing the charging load active power of the electric automobile at a node m; n is a radical of d Representing the number of nodes of the power distribution network;
(2) the voltage risk index of the power distribution network adopts the following formula:
δ(U m )＝|U m -1| (9)
wherein n is a distribution network voltage risk indicator, delta (U) m ) Is the amount of voltage deviation at the node m,
is the severity coefficient, S δ (U m ) Is the severity of the voltage deviation at node m, and α and β are weighting factors.
4) Establishing an index set of random variables in a probability space of the power distribution network according to the randomness parameters of the power distribution network provided in the step 1), and dividing a subset and a complementary set of random variable indexes; selecting an orthogonal polynomial base according to the probability distribution of the load, the illumination intensity and the charging load of the electric automobile in the step 1), establishing a low-rank approximation model of the voltage risk index of the power distribution network according to mutually independent random variable samples 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 the content of the first and second substances,
(1) the establishing of the index set of the random variables in the probability space of the power distribution network and the dividing of the subsets and the complementary sets of the random variable indexes specifically comprise:
ξ＝(ξ 1 ,ξ 2 ,…,ξ n ) If the random variables are random variables in the probability space of the power distribution network, the index set of the random variables in the probability space of the power distribution network is delta {1,2, …, n }, and n is the total number of the random variables; setting random variable index subset k ═ i 1 ,…,i s Is equal to or greater than 1 and is equal to or less than n, then is k Is a non-empty subset with k as a ξ index subset and a random variable index complement
(2) The low-rank approximation model of the voltage risk index of the power distribution network is expressed as follows:
in the formula, h is a distribution network voltage risk index,
is a low-rank approximation estimation of the voltage risk indicator of the distribution network, b l Is the normalized weight factor, ω, for a rank of l l (xi) is a rank-one function of a random variable xi in the probability space of the distribution network when the rank is l,
is the ith random variable xi in the probability space of the distribution network when the rank is l i R is the maximum expansion rank number of the low-rank approximation estimation;
will be provided with
At the base of a polynomial orthogonal to the corresponding probability distribution
And (3) expanding, and further expressing a low-rank approximation model of the voltage risk index of the power distribution network as follows:
in the formula (I), the compound is shown in the specification,
is the ith random variable xi in the probability space of the distribution network i The (q) th order polynomial of (1),
is the ith random variable xi in the probability space of the distribution network when the rank is l i The q-th order polynomial coefficient of (a), γ 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) design of experiment considering random variable sample size N, including random variable sample xi N ＝(ξ (1) ,…,ξ (N) ) And distribution network voltage risk index sample h N ＝(h (1) ,…,h (N) ) (ii) a Given a maximum expansion rank r of low-rank approximation estimation and a maximum expansion order gamma of a polynomial, the set maximum iteration number is I max Setting the maximum relative iteration error to e max (ii) a Initializing a rank number l ═ 1;
(3.2) judging whether the current rank l is greater than the given low-rank approximation estimation maximum expansion rank r or not, if so, ending, and if not, entering the step (3.3);
(3.3) number of initialization iterations I l Initializing relative iteration error as 0
(3.4) judging the relative iteration error
Whether the maximum iteration error is less than the set maximum iteration error to be e max Or number of iterations I l Whether the number of iterations is greater than the set maximum number of iterations I max If yes, entering the step (3.9), and if not, entering the step (3.5);
(3.5) number of iterations I l ＝I l +1；
(3.6) for ith random variable xi in probability space of power distribution network i (i ═ 1, …, n), and a rank one function omega of a random variable xi in a probability space of the distribution network when the rank is l is solved by adopting an alternating least square method l (xi) the minimization problem described by the equation (17) converted into the equation (18) is solved to obtain the rankIs the ith random variable xi in the probability space of the distribution network at the time of l i Polynomial coefficient of
Then updated by equation (19)
In the formula (I), the compound is shown in the specification,
representing the residual error h of the voltage risk index h of the distribution network when the rank is (l-1) (t) Representing a tth distribution network voltage risk indicator sample,
denotes the sample ξ at the tth random variable when the rank is (l-1) (t) Estimating the low-rank approximation of the voltage risk index of the upper distribution network; w represents a rank vector space, ω is an optimization variable in W; r γ Representing the gamma-order polynomial coefficient space, k q Is R γ With the optimizing variable in (K) being R γ The set of optimization variables in (1);
(3.7) solving by using the formula (20) to obtain a rank-one function omega of a random variable xi in a probability space of the power distribution network when the rank is l l (ξ)：
(3.8) calculating the relative iteration error using equation (21)
Then entering the step (3.4):
in the formula (I), the compound is shown in the specification,
the relative iteration error is represented as a function of,
representing the variance calculation;
(3.9) solving equation (22), which describes the minimization problem, as follows, to obtain a normalized weight factor set b ═ b 1 ,…,b l }：
In the formula, R l Normalized weight factor space, ψ, when the rank is l l Is R l Where the optimizing variable ψ is R l The set of optimization variables in (1);
(3.10) calculating a low-rank approximation estimation of the voltage risk indicator of the power distribution network by using the following formula (23), and then entering the step (3.2):
in the formula (I), the compound is shown in the specification,
is a low-rank approximation estimation of the voltage risk indicator of the distribution network when the rank is l, b π Is a normalized weight factor, ω, for a rank of π π (xi) is a rank-one function of a random variable xi in the probability space of the distribution network when the rank is pi.
In the embodiment, the uncertainty conduction capability of the low-rank approximation model is described by taking the voltage assignment of the power distribution network node 18 as an example, in the embodiment, the probability density distribution and the cumulative distribution function 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 results of the low-rank approximation model and the monte carlo method are similar, and the out-of-limit probability of the node 18 voltage exceeds 30%.
5) Generating mutually independent random variable samples in two groups of standard normal spaces by adopting a quasi-Monte Carlo method, 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 voltage risk index of the power distribution network obtained in the step 4); the method comprises the following steps:
obtaining an expression form of the voltage risk index of the power distribution network based on variance decomposition by adopting the following formula:
in the formula, h (xi) is a distribution network voltage risk index considering the influence of a random variable xi in a distribution network probability space, and h (xi) is 0 A desire to represent h (ξ); k and v represent index subsets of random variable xi in probability space of distribution network k And xi v Is a non-empty subset h of a random variable xi in the probability space of the distribution network k (ξ k ) And h v (ξ v ) Respectively representing consideration xi k And xi v The voltage risk indicator of the power distribution network is influenced;
indicating the desired operation.
The variance D of h (ξ), expressed as:
wherein D represents the variance of h ([ xi ]), and D k Non-null subset xi representing random variable xi in probability space of distribution network k The variance of (a) is determined,
representing the variance calculation;
non-null subset xi of random variable xi in probability space of power distribution network k The global sensitivity of (a) is calculated by the following formula:
in the formula, S k Non-null subset xi representing random variable xi in probability space of distribution network k The interaction-influencing factor(s) of (c),
non-null subset xi representing random variable xi in probability space of distribution network k The global sensitivity of (c);
order to
Wherein
Is expressed in xi k The expected value of h (ξ) for the condition. Due to the fact that
Therefore, the nonempty subset xi of the random variable xi in the probability space of the distribution network k Global sensitivity of
Further expressed as:
the two situations that components in a random variable xi in a probability space of a power distribution network are independent from each other and have correlation are discussed respectively:
(1) when all components in the random variable xi in the probability space of the power distribution network are mutually independent, the non-null subset xi of the random variable xi in the probability space of the power distribution network based on the low-rank approximation model k Global sensitivity of
Is calculated as follows:
in the formula
Non-null subset xi representing random variable xi in power distribution network probability space based on low rank approximation model k Global sensitivity of h LRA (xi) represents a distribution network voltage risk index considering the influence of a random variable xi in a distribution network probability space based on a low rank approximation model,
is expressed in xi k Is a condition of h LRA (xi) a desired value;
calculating the relationship by the following according to the orthogonality of the probability distribution corresponding polynomial:
to obtain
In the calculation formula
And
the analytical formula (2) is as follows:
in the formula, xi i And xi j Respectively the ith and jth random variables in the probability space of the distribution network,
and
the method is characterized in that ith random variable xi in probability space of the power distribution network is respectively when the rank is l and the rank is m i A univariate function of (a);
is the ith random variable xi in the probability space of the distribution network when the rank is l i The coefficient of the 0 th order polynomial of (a),
and
the ith random variable xi in the probability space of the distribution network is respectively when the rank is l and when the rank is m i The coefficient of the kth-order polynomial of (c),
and
the ith random variable xi in the probability space of the power distribution network is respectively when the rank is l and when the rank is m i The qth polynomial coefficient of (1); b l And b m The normalization weight factors are respectively when the rank is l and when the rank is m; r is the maximum expansion order number of low-rank approximation estimation, n is the total number of random variables, and gamma is the maximum expansion order number of a polynomial;
(2) when each component in the random variable xi in the probability space of the power distribution network has correlation, the non-empty subset xi of the random variable xi in the probability space of the power distribution network based on the Monte Carlo method k Global sensitivity of
Is calculated as follows:
in the formula, a random variable xi ═ in the probability space of the distribution network (xi) k ,ξ w )，ξ k And xi w Are two complementary subsets of ξ;
and
conditional probability distribution representing probability space of slave distribution network
Two groups of different random variable subsets obtained by middle sampling;
representing random variables in probability space of power distribution network
The voltage risk indicator of the power distribution network is influenced;
therefore, nonempty subset xi of random variable xi in probability space of power distribution network based on low rank approximation model k Global sensitivity of
The calculation formula of (a) is as follows:
in the formula, ζ represents a random variable in a normalized normal space where ξ is subjected to the Natta conversion, and ζ represents k Xi show k Random variable in standard normal space, ζ 'obtained by Natta conversion' w To represent
Random variables in the standard normal space obtained by the naf transform.
The photovoltaic at the distribution network node 18 in the embodiment is taken as an example to illustrate the accuracy and the solving efficiency of solving the global sensitivity based on the low-rank approximation model. In the embodiment, the convergence relationship between the global sensitivity of the photovoltaic at the distribution network node 18 and the sampling number is shown in fig. 4, and it can be seen that the convergence can be stably performed based on the low-rank approximation model method, and the convergence accuracy is close to that of the monte carlo method. The global sensitivity calculation efficiency ratio of the photovoltaic at the node 18 is shown in table 6, and it can be seen that the low-rank approximation model solving efficiency is high in the monte carlo method, and the method has advantages in the aspects of model building and evaluation solving compared with the polynomial chaotic expansion method. The global sensitivity of the random variable of the distribution network in the embodiment is shown in fig. 5.
TABLE 6 Global sensitivity calculation efficiency comparison of photovoltaics 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 influencing the voltage risk indexes of the power distribution network.
For an embodiment of the invention, the converter reactive capacity is configured according to 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 the effectiveness of the method for identifying the key uncertain factors of the distribution network containing the high-proportion photovoltaic power generation system and the electric automobile, the following 5 scenes are adopted for verification and analysis in the embodiment:
scene I: in an original scene, a 52-dimensional random variable is considered, and the photovoltaic reactive capacity is not configured;
scene II: taking a threshold value of 0.015, and only considering 14-dimensional random variables with global sensitivity larger than the threshold value;
scene III: only photovoltaic configuration converter reactive capacity with the maximum global sensitivity;
scene IV: configuring the reactive capacity of a current converter in the first 4 photovoltaic configurations with the maximum global sensitivity;
scene V: and configuring the reactive capacity of the converter at all the photovoltaic regions.
In the embodiment, the cumulative distribution function of the voltage risk indexes before and after the dimensionality reduction of the power distribution network is shown in fig. 6, it can be seen that only the random variable with higher global sensitivity is reserved, the random variable with lower global sensitivity is used as a deterministic variable to be processed, and the uncertainty of the system is reduced while the solving precision is ensured.
The system voltage distribution under the condition that the reactive capacity of the photovoltaic converter is not configured in the power distribution network in the embodiment and the system voltage distribution under the condition that the reactive capacity of the photovoltaic converter is configured at the first 4 nodes with the maximum global sensitivity are respectively shown in fig. 7a and 7b, and it can be seen that the system voltage distribution is remarkably improved by configuring the reactive capacity of the photovoltaic converter at the first 4 nodes with the maximum global sensitivity.
In the embodiment, the distribution network voltage risk index probability density distribution and the cumulative distribution function are respectively shown in fig. 8a and fig. 8b, it can be seen that the effect of the reactive capacity of the first 4 photovoltaic configuration converters with the maximum global sensitivity on reducing the distribution network voltage risk index is similar to the effect of the reactive capacity of all the photovoltaic configuration converters, and the investment is less, so that the provided identification method for the key uncertain factors of the distribution network containing high-proportion photovoltaic and electric vehicles can provide guidance for the configuration of the reactive capacity of the photovoltaic converters.
Claims (5)
1. A method for identifying key uncertain factors of a power distribution network containing high-proportion photovoltaic and electric vehicles is characterized by comprising the following steps:
1) inputting a power distribution network deterministic parameter and a power distribution network randomness parameter according to the selected power distribution network; the power distribution network certainty parameters comprise a network topology connection relation, a line resistance reactance, a load rated power and an installation position, a photovoltaic installation capacity and an installation position, and an installation capacity and an installation position of an electric automobile charging load; the randomness parameters of the power distribution network 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 probability space of the power distribution network;
2) according to the power distribution network randomness parameters provided in the step 1), loads, illumination intensity and electric vehicle charging loads are used as random variables xi in a power distribution network probability space, a quasi-Monte Carlo method is adopted to obtain mutually independent random variable samples in a standard normal space, and Naphv transformation is utilized to obtain the random variable samples in the power distribution network probability space;
3) establishing a power distribution network deterministic load flow calculation model according to the power distribution network deterministic parameters 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 power distribution network probability space 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 randomness parameters of the power distribution network provided in the step 1), and dividing a subset and a complementary set of random variable indexes; selecting an orthogonal polynomial base according to the probability distribution of the load, the illumination intensity and the charging load of the electric automobile in the step 1), establishing a low-rank approximation model of the voltage risk index of the power distribution network according to mutually independent random variable samples 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, 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 voltage risk index of the power distribution network 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 influencing the voltage risk indexes of the power distribution network.
2. The method for identifying key uncertain factors of power distribution networks containing high-proportion photovoltaic power and electric vehicles according to claim 1, wherein the step 2) of obtaining random variable samples in the probability space of the power distribution network by using the Natta transformation specifically comprises the following steps:
according to the correlation coefficient rho between random variables in the probability space of the power distribution network ij Solving the correlation coefficient matrix rho in the standard normal space φ ：
In the formula (I), the compound is shown in the specification,
is the ith random variable in the standard normal space
The cumulative distribution function of; g i (ξ i ) Is the ith random variable xi in the probability space of the distribution network i The cumulative distribution function of;
is the ith random variable in the standard normal space
And jth random variable
The correlation coefficient of (1), i.e. the matrix of correlation coefficients p in the normal space φ Row i and column j elements of (1); ρ is a unit of a gradient ij Is the ith random variable xi in the probability space of the distribution network i And j-th random variable ξ j The correlation coefficient of (a); phi is a 2 Is a probability density function of 2-dimensional standard normal distribution; mu.s i And mu j Respectively is the ith random variable xi in the probability space of the distribution network i And j-th random variable ξ j Expectation of (a) i And σ j Respectively is the ith random variable xi in the probability space of the distribution network i And j-th random variable ξ j Standard deviation of (d);
relating the matrix rho of the relation number in the standard normal space φ Performing square root decomposition, and obtaining a random variable xi (xi) in the probability space of the power distribution network according to independent random variable zeta samples in the standard normal space 1 ，ξ 2 ，…，ξ n ) Samples, as follows:
ρ φ ＝LL T (3)
in the formula, L represents a lower triangular matrix, and ζ represents mutually independent random variables in a standard normal space.
3. The method for identifying key uncertain factors of power distribution networks containing high-proportion photovoltaic power and electric vehicles according to claim 1, wherein the deterministic power flow calculation model of the power distribution network in the step 3) is represented as follows:
in the formula (I), the compound is shown in the specification,
representing state variables of the power distribution network, including a node voltage phase angle theta and an amplitude value U; xi ═ P Load ，P EV ，τ] T Representing random variables in the probability space of the distribution network, including the load active power P Load Active power P of charging load of electric automobile EV And the illumination intensity τ; p m Injecting active power, Q, for node m in a power distribution network m Injecting reactive power, theta, for node m in a distribution network mc Is the voltage phase angle difference of node m and node c; u shape m And U c The voltage amplitudes, G, of node m and node c, respectively mc And B mc The real part and the imaginary part of the mth row and the mth column of the element of the power distribution network node admittance matrix are respectively.
And
respectively representing active power and reactive power transmitted by the transformer substation from a node m;
and
respectively representing the active power and the reactive power of the node m load;
representing the intensity of illumination tau at node m m The active power of the photovoltaic under the condition,
representing the charging load active power of the electric automobile at a node m; n is a radical of d Representing the number of nodes of the power distribution network;
the voltage risk index of the power distribution network adopts the following formula:
δ(U m )＝|U m -1| (9)
in the formula, h is a distribution network voltage risk index, delta (U) m ) Is the amount of voltage deviation at the node m,
is the severity coefficient, S δ (U m ) Is node m voltage biasPoor severity, α and β are weighting coefficients.
4. The method for identifying the key uncertain factors of the distribution network containing the high-proportion photovoltaic power and the electric vehicle according to claim 1, wherein the step 4) is implemented by establishing an index set of random variables in a probability space of the distribution network and dividing a subset and a complementary set of the random variable indexes, and specifically comprises the following steps:
ξ＝(ξ 1 ，ξ 2 ，…，ξ n ) If the random variables are random variables in the probability space of the power distribution network, the index set of the random variables in the probability space of the power distribution network is delta {1,2, …, n }, and n is the total number of the random variables; setting a random variable index subset k ═ i 1 ，…，i s Is equal to or greater than 1 and is equal to or less than n, then is k Is a non-empty subset with k as a ξ index subset and a random variable index complement
The low-rank approximation model of the voltage risk index of the power distribution network is expressed as follows:
in the formula, h is a distribution network voltage risk index,
is a low-rank approximation estimation of the voltage risk indicator of the distribution network, b l Is a normalized weight factor, ω, for a rank of l l (xi) is a rank-one function of a random variable xi in the probability space of the distribution network when the rank is l,
is the ith random variable xi in the probability space of the distribution network when the rank is l i R is the maximum expansion rank number of the low-rank approximation estimation;
will be provided with
At polynomial bases orthogonal to the corresponding probability distributions
And (3) expanding, and further expressing a low-rank approximation model of the voltage risk index of the power distribution network as follows:
in the formula (I), the compound is shown in the specification,
is the ith random variable xi in the probability space of the distribution network i The (q) th order polynomial of (1),
is the ith random variable xi in the probability space of the distribution network when the rank is l i The q-th order polynomial coefficient of (a), γ 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) design of experiment considering random variable sample size as N, including random variable sample xi N ＝(ξ (1) ，…，ξ (N) ) And distribution network voltage risk index sample h N ＝(h (1) ，…，h (N) ) (ii) a Given a maximum expansion rank r of low-rank approximation estimation and a maximum expansion order gamma of a polynomial, the set maximum iteration number is I max Setting the maximum relative iteration error to e max (ii) a Initializing a rank number l as 1;
(2) judging whether the current rank number l is greater than a given low-rank approximate estimation maximum expansion rank number r or not, if so, ending, and if not, entering the step (3);
(3) number of initialization iterations I l Initializing relative iteration error as 0
(4) Determining relative iteration error
Whether the maximum iteration error is less than the set maximum iteration error to be e max Or number of iterations I l Whether the number of iterations is greater than the set maximum number of iterations I max If yes, entering the step (9), and if not, entering the step (5);
(5) number of iterations I l ＝I l +1；
(6) For ith random variable xi in probability space of power distribution network i (i ═ 1, …, n), and a rank one function omega of a random variable xi in a probability space of the distribution network when the rank is l is solved by adopting an alternating least square method l Converting the formula (17) of the (xi) into a minimization problem described by the formula (18) to solve to obtain the ith random variable xi in the probability space of the power distribution network when the rank is l i Polynomial coefficient of
Then updated by equation (19)
In the formula (I), the compound is shown in the specification,
representing the residual error h of the voltage risk index h of the distribution network when the rank is (l-1) (t) Representing a tth distribution network voltage risk indicator sample,
denotes the sample ξ at the tth random variable when the rank is (l-1) (t) Estimating the low-rank approximation of the voltage risk index of the upper distribution network; w represents a rank vector space, ω is an optimization variable in W; r γ Representing a gamma-order polynomial coefficient space, κ q Is R γ With the optimizing variable in (K) being R γ The set of optimization variables in (1);
(7) solving by using the formula (20) to obtain a rank-one function omega of a random variable xi in a probability space of the power distribution network when the rank is l l (ξ)：
(8) Calculating the relative iteration error using equation (21)
Then entering the step (4):
in the formula (I), the compound is shown in the specification,
the relative iteration error is represented as a function of,
representing the variance calculation;
(9) solving equation (22), which describes the minimization problem, as follows, results in a set of normalized weight factors, b ═ b 1 ，…，b l }：
In the formula, R l Normalized weight factor space, ψ, when the rank is l l Is R l Where the optimizing variable ψ is R l The set of optimization variables in (1);
(10) calculating a low-rank approximation estimation of the voltage risk index of the power distribution network by using the following formula (23), and then entering the step (2):
in the formula (I), the compound is shown in the specification,
is a low-rank approximation estimation of the voltage risk indicator of the distribution network when the rank is l, b π Is a normalized weight factor, ω, for a rank of π π (xi) is a rank-one function of a random variable xi in the probability space of the distribution network when the rank is pi.
5. The method for identifying key uncertain factors of power distribution network containing high-proportion photovoltaic power and electric vehicles according to claim 1, wherein the step 5) comprises the following steps:
obtaining an expression form of the voltage risk index of the power distribution network based on variance decomposition by adopting the following formula:
in the formula, h (xi) is a distribution network voltage risk index considering the influence of a random variable xi in a distribution network probability space, and h (xi) is 0 A desire to represent h (ξ); k and v represent index subsets of random variable xi in probability space of distribution network k And xi v Is a non-empty subset h of a random variable xi in the probability space of the distribution network k (ξ k ) And h v (ξ v ) Respectively representing consideration xi k And xi v The voltage risk indicator of the power distribution network is influenced;
indicating the desired operation.
The variance D of h (ξ), expressed as:
wherein D represents the variance of h ([ xi ]), and D k Non-null subset xi representing random variable xi in probability space of distribution network k The variance of (a) is determined,
representing the variance calculation;
non-null subset xi of random variable xi in probability space of power distribution network k The global sensitivity of (a) is calculated by the following formula:
in the formula, S k Non-null subset xi representing random variable xi in probability space of distribution network k The interaction-influencing factor(s) of (c),
non-null subset xi representing random variable xi in probability space of distribution network k The global sensitivity of (c);
order to
Wherein
Is expressed in xi k The expected value of h (ξ) under this condition. Due to the fact that
Therefore, the nonempty subset xi of the random variable xi in the probability space of the distribution network k Global sensitivity of
Further expressed as:
the two situations that components in a random variable xi in a probability space of a power distribution network are independent from each other and have correlation are discussed respectively:
(1) when all components in the random variable xi in the probability space of the power distribution network are mutually independent, the non-null subset xi of the random variable xi in the probability space of the power distribution network based on the low-rank approximation model k Global sensitivity of
Is calculated as follows:
in the formula
Non-null subset xi representing random variable xi in power distribution network probability space based on low rank approximation model k Global sensitivity of h LRA (xi) represents a distribution network voltage risk index considering the influence of a random variable xi in a distribution network probability space based on a low rank approximation model,
is expressed in xi k Is a condition of h LRA (ξ) a desired value;
calculating the relationship by the following according to the orthogonality of the probability distribution corresponding polynomial:
to obtain
In the calculation formula
And
the analytical formula (2) is as follows:
in the formula, xi i And xi j Respectively the ith and jth random variables in the probability space of the distribution network,
and
the method is characterized in that ith random variable xi in probability space of the power distribution network is respectively when the rank is l and the rank is m i A univariate function of (a);
is the ith random variable xi in the probability space of the distribution network when the rank is l i The coefficient of the 0 th order polynomial of (a),
and
the ith random variable xi in the probability space of the power distribution network is respectively when the rank is l and when the rank is m i The coefficient of the kth-order polynomial of (c),
and
the ith random variable xi in the probability space of the power distribution network is respectively when the rank is l and when the rank is m i The qth polynomial coefficient of (1); b l And b m The normalization weight factors are respectively when the rank is l and when the rank is m;r is the maximum expansion order number of low-rank approximation estimation, n is the total number of random variables, and gamma is the maximum expansion order number of a polynomial;
(2) when each component in the random variable xi in the probability space of the power distribution network has correlation, the non-empty subset xi of the random variable xi in the probability space of the power distribution network based on the Monte Carlo method k Global sensitivity of
Is calculated as follows:
in the formula, a random variable xi ═ in the probability space of the distribution network (xi) k ，ξ w )，ξ k And xi w Are two complementary subsets of ξ;
and
conditional probability distribution representing probability space of slave distribution network
Two groups of different random variable subsets obtained by middle sampling;
random variable in probability space of power distribution network is considered in representation
The voltage risk indicator of the power distribution network is influenced;
therefore, nonempty subset xi of random variable xi in probability space of power distribution network based on low rank approximation model k Global sensitivity of
The calculation formula of (a) is as follows:
in the formula, ζ represents a random variable in a normalized normal space where ξ is subjected to the Natta conversion, and ζ represents k Xi show k Random variable in standard normal space, ζ 'obtained by Natta conversion' w To represent
Random variables in the standard normal space obtained by the naf transform.
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