A Method for Modeling the Probability of Distributed Photovoltaic Spatial Correlation Output

Abstract

The present invention relates to the field of photovoltaic technology, and in particular to a method for modeling the probability of spatially correlated output of distributed photovoltaics, including: S1, determining the empirical correlation between the clear sky indices at N positions to obtain a correlation matrix; S2, using the correlation matrix to define a multivariate Gaussian distribution; S3, extracting samples from the multivariate Gaussian distribution; S4, obtaining the relevant uniform distribution values from the univariate Gaussian cumulative distribution function; S5, obtaining relevant samples from the distribution of the clear sky index; S6, establishing a probability model for the output of distributed photovoltaics considering spatial correlation. The method for modeling the output of distributed photovoltaics studying spatial correlation according to the present invention can further explore the influence of the correlation between the outputs of distributed power sources on the consumption potential of the distribution network, and at the same time improve the accuracy of the modeling of the output of distributed power sources by using the Gaussian Copula function, providing guidance for the distribution network planning to promote the consumption of new energy.

Description

Technical Field

[0001] The present invention relates to the technical field of photovoltaic technology, and particularly to a method for modeling the probability of spatially correlated output of distributed photovoltaics. Background Art

[0002] In traditional distribution networks, the power flow is unidirectional, and the planning is mainly driven by meeting the load demand. The distribution network planning considers how to determine the network structure, power source capacity and location on the premise of meeting the rapid growth of load demand. In the future distribution network with high renewable energy penetration, due to the large access of renewable energy, the distribution network changes from the traditional single radial structure to a multi-source structure, and the operating characteristics of the distribution network are thus significantly affected. Many problems such as overvoltage and reverse power flow will have a negative impact on the system operation. In order to meet the demand for more renewable energy access, the original distribution network planning and operation mode of simple load-driven mode will no longer meet the current situation. It is necessary to evaluate the system's ability to carry these distributed power sources and make reasonable planning without exceeding the system operation performance limit. Photovoltaic is the main carrier of renewable energy utilization. Therefore, studying the output characteristics of photovoltaics and accurately constructing a photovoltaic output model are of great significance for the planning, dispatching and evaluation of distribution networks. Summary of the Invention

[0003] The technical problem to be solved by the present invention is: considering that the existing photovoltaic output model does not consider the influence of spatial distance on irradiance, a spatially correlated distributed photovoltaic output probability model is established through the Copula theory.

[0004] The technical solution adopted by the present invention is: a method for modeling the probability of spatially correlated output of distributed photovoltaics includes the following steps:

[0005] S1. Determine the empirical correlation between the clear sky indices at N positions to obtain the correlation matrix P;

[0006] The change in solar irradiance of N photovoltaic sites in the spatial network is simulated by the instantaneous clear sky index, defined as the ratio of the ground horizontal irradiance G i (t) of the i-th site to the ground horizontal clear sky irradiance G c，i (t) at the same site at time t:

[0007]

[0008] Normalizing the irradiance to the clear sky irradiance is to eliminate the time correlation caused by the obvious movement of the sun and the deterministic change of irradiance; the remaining random change (ideally) is only related to the fluctuation of cloud cover;

[0009] Take the instantaneous clear sky index of each site as the random variable X i, each random variable has its own probability distribution; the random variable X 1 , ..., X N 's specific realization can be regarded as a snapshot of the network at an unspecified time point, where N probability distributions specify the possible values that the clear-sky index can take at each site at this time; therefore, a set of independent X 1 , ..., X N realizations can be used to represent the clear-sky index of the site at any time point without considering the time series; at a given site and time, the probability distribution of solar irradiance (rather than the clear-sky index) can be represented by X i G c，i (t), where G c，i (t) gives the scalar value of the determined clear-sky irradiance at time t.

[0010] Define the total clear-sky index, which represents the average instantaneous irradiance of all sites in the power grid:

[0011]

[0012] 1. Assume that the locations of these sites are close enough so that the clear-sky irradiance of all stations is equal, that is, G c，i (t) ≡ G c (t), i = 1, ..., N;

[0013] 2. Since it is assumed that the observation stations are close to each other, it is assumed that the probability distributions of the global irradiance are equal, that is, it is assumed that all observation stations are affected by the same cloud pattern and cloud movement; therefore, all random variables X 1 , ..., X N are modeled with the same probability distribution, and its cumulative distribution function is represented by F X (x);

[0014] The correlation between random variable pairs is modeled using the Pearson correlation coefficient:

[0015]

[0016] where Cov(X i , X j ) is the covariance of X i and X j , σ i , σ j are the corresponding standard deviations; if the clear-sky indices observed by a pair of observation stations are always the same, the correlation coefficient is 1; on the contrary, if the correlation coefficient is zero, it means that the cloud cover between the two observation stations is completely randomly distributed; the overall correlation structure between all site pairs can be represented by a correlation matrix:

[0017]

[0018] When modeling the correlation for any network configuration, an exponential decay model of site pair correlation is used:

[0019] ρ(Δx) = e -γΔx (5)

[0020] where γ is a parameter that determines how fast the correlation decays with distance, and Δx is the distance between two sites.

[0021] S2. Define the multivariate Gaussian distribution N(μ, P) using the correlation matrix, μ = [μ 1 ,... μ N , μ i ≡ 0;

[0022] The Copula function can connect the joint distribution function of multidimensional random variables with their respective marginal distribution functions, and is mainly used to describe the correlation between random variables. The distribution function in probability theory is the most fundamental method to describe the correlation (including the correlation structure) of random variables. However, in practical applications, the analytical formula of the joint distribution function is difficult to handle, and the solution process requires that the types of each marginal distribution function and the joint distribution function be the same. The Copula function is a class of functions that connect the joint distribution function of variables with their respective marginal distribution functions, providing a flexible method for obtaining the joint distribution function.

[0023] Using the Copula model can generate data of the clear sky index and finally generate data of solar irradiance, taking into account the possible correlation between the distances of different observation stations. The basic idea is to find a method that can randomly sample the clear sky index of different observation stations while ensuring that these samples are correlated. For two stations close in location, the sampled values should be very similar; while for stations far apart, the sampled values should be allowed to vary within a larger range.

[0024] When randomly sampling values from a univariate distribution, the inversion method is usually adopted. Since X is a random variable with a cumulative distribution function F X and U is a random variable uniformly distributed on [0, 1], the random variable and X have the same distribution; that is, randomly sampling a number u from the distribution of U, a sample of the X distribution obtained is:

[0025]

[0026] Conversely, that is, the distribution of the random variable is uniform, so inputting x from the distribution of X to results in a uniform distribution of u.

[0027] Suppose it is necessary to sample from several different distributions to obtain their respective correlation values. It is necessary to sample from to obtain the sample x 1 ,..., x n , where the uniform distribution values u 1 ,..., u N corresponding to all samples have their respective specific correlations.

[0028] S3. Sample from the multivariate Gaussian distribution N(μ, P), μ = [μ 1 ,..., μ N , μ i ≡0 to obtain the samples v 1 ,..., v N ;

[0029] S4. Obtain the relevant uniform distribution value u i =Φ(v i ), i = 1,..., N;

[0030] By combining the Gaussian cumulative distribution function, the uniform distribution value that retains the correlation can be obtained:

[0031] u i =Φ(v i ) (7)

[0032] S5. Obtain the relevant samples from the distribution of the clearness index

[0033] Adopt the Gaussian Copula and define the joint cumulative distribution function of the uniform distribution random variables U 1 ,..., U N as C(u 1 ,..., u N ); Since these uniform random variables can be given by different distribution functions , the Copula can connect several different distributions and give their multivariate cumulative distribution function:

[0034]

[0035] According to Sklar's theorem, any multivariate distribution function can be represented by the Copula combined with its marginal distribution functions;

[0036] S6. Convert the clearness index into the photovoltaic power injected into the distribution network bus. According to the output data of the grid-connected distributed photovoltaic power station, establish a probability model of distributed photovoltaic output considering spatial correlation;

[0037] The clearness index can be converted into the photovoltaic power injected into the distribution network bus; first, the clearness index must be multiplied by the clear sky irradiance at a certain time and location to obtain the ground surface horizontal irradiance:

[0038] G = kG c (9)

[0039] where G c is the clear sky irradiance, and then the irradiance must be decomposed into direct and diffuse irradiances:

[0040] G d = k d G, G b = G - G d (10)

[0041] where k d is the scattering fraction, modeled as a function of the clearness index (the ratio of ground surface irradiance to extraterrestrial irradiance); then these components need to be converted into parameters in any direction of the photovoltaic system; this is done using the standard angle of incidence formula and the Hay and Davies model, which is used to convert to an inclined plane:

[0042]

[0043] where the geometric factor R b is the direct irradiance proportionality factor based on the radiation angle of incidence on the inclined and horizontal planes; β is the inclination angle of the photovoltaic panel; ρ g is the ground surface reflectivity;

[0044] The DC power output of the photovoltaic array on the inclined plane is determined using a simplified model as:

[0045] P dc = AG T η(1 - q a ) (12)

[0046] where A is the total area of the photovoltaic array; η is the conversion efficiency of the photovoltaic module; q a is the additional loss rate;

[0047] The AC power output by the inverter of the photovoltaic system is determined based on the Sandia inverter model:

[0048]

[0049] P ac0 is the rated maximum AC power of the inverter; P dc0 is the DC power when the inverter reaches the AC rated power; P s0 is the threshold power of the inverter, at which it starts to provide an AC output;

[0050] Therefore, the clear sky index can be converted into the photovoltaic power injected into the distribution network bus. By obtaining the output data of grid-connected distributed photovoltaic power stations in a certain area, a probability model of distributed photovoltaic output considering spatial correlation can be established.

[0051] Advantages of the present invention:

[0052] 1. Studying the modeling method of distributed photovoltaic output considering spatial correlation can further explore the impact of the correlation between distributed power outputs on the consumption potential of the distribution network. At the same time, using the Gaussian Copula function can improve the accuracy of distributed power output modeling, providing guidance for the distribution network planning to promote new energy consumption. Description of the drawings

[0053] Figure 1 is the flowchart of the method for probability modeling of distributed photovoltaic spatial correlation output of the present invention;

[0054] Figure 2 is the geographical location map of distributed photovoltaic power stations in Area A and Area B of a certain city of the present invention;

[0055] Figure 3 is the correlation matrix of distributed photovoltaic outputs in Area A and Area B of the present invention;

[0056] Figure 4 is the empirical curve of the correlation between photovoltaic output and distance in a certain city of the present invention. Specific embodiments

[0057] The present invention will be further described below with reference to the drawings and embodiments. This figure is a simplified schematic diagram, which only illustrates the basic structure of the present invention in a schematic manner. Therefore, it only shows the components related to the present invention.

[0058] As Figure 1 shown, a method for probability modeling of distributed photovoltaic spatial correlation output includes the following steps:

[0059] S1. Determine the empirical correlation between N location clear sky indices to obtain the correlation matrix P;

[0060] The present invention first establishes the relationship between the correlation coefficient of photovoltaic output and the spatial distance through the historical data set of a region in a certain city; then, based on the spatial distance correlation coefficient relationship, uses the Gaussian Copula to establish the joint distribution of the benchmark distributed PV (photovoltaic) at any geographical location; finally, proposes a method for generating relevant PV output samples from the joint probability distribution.

[0061] The data for the study were from 18 grid-connected distributed photovoltaic power stations in a certain city; due to the influence of the subtropical monsoon climate, cumulus and fractus clouds often appear in this city area, resulting in significant and frequent changes in the input photovoltaic output; the measured photovoltaic arrays were located in two areas of a certain city: Area A and Area B, and these distributed PV sites were distributed in areas of about 10 km and 15 km, numbered 1 - 10 and 11 - 18 respectively, as Figure 2 shown; in 2018, the photovoltaic power generation of each power station was measured and recorded every 5 minutes.

[0062] To eliminate the useless zero PV output at night, only the data from 9 am to 3 pm were used every day; in addition, to avoid the influence of bad data, the time periods with zero PV output during the day were omitted in the test, which resulted in a dataset of 19149 data points for each location; since we are concerned about the correlation and volatility of the PV output, by normalizing the capacity of the PV output, the influence of the photovoltaic installed capacity can be ignored; as Figure 3 shown, Figure 3 The upper half of the figure shows the correlation matrix and distance matrix of Area A in a certain city as shown in Figures (a) and (b) respectively, Figure 3 The lower half of the figure shows the correlation matrix and distance matrix of Area B in a certain city as shown in Figures (c) and (d) respectively;

[0063] It can be seen that the correlation coefficient of the PV output matrix has a strong relationship with the distance between photovoltaic power stations, that is, the shorter the distance between adjacent locations, the higher the correlation.

[0064] S2. Use the correlation matrix to define the multivariate Gaussian distribution N(μ, P), μ = [μ 1 ,..., μ N , μ i ≡ 0;

[0065] S3. Extract samples v 1 ,..., v N from the multivariate Gaussian distribution;

[0066] S4. Obtain the relevant uniform distribution values u i = Φ(v i ), i = 1,... N;

[0067] S5. Obtain relevant samples from the distribution of the clear sky index

[0068] The PV output of each photovoltaic station can be regarded as a random variable x i , and its cumulative distribution function is Fx i (x i ), where x i is x isample set; Since the distribution system usually covers a small geographical area, it is assumed that PV stations are affected by the same type of cloud patterns and cloud movements; Therefore, all random variables x 1 , …, x N can all be modeled with the same probability distribution F x (x);

[0069] Then, the Pearson correlation coefficient is used to represent the linear correlation between PV stations using formula (3), and the relationship between the correlation coefficient and distance can be expressed by equation (14);

[0070] ρ ij = f(ξ ij ) (14)

[0071] ξ ij is the distance between two PV stations, and equation (14) gives the general form of the relationship between spatial correlation and distance; The specific form of equation (14) should be determined according to the historical values of local photovoltaic power generation and the actual distance between them; Taking the data set of a certain city as an example, the present invention gives the fitting results, as Figure 4 shown: It can be seen from Figure 4 that there is a certain relationship between geographical distance and the correlation coefficient of photovoltaic output; The relationship between geographical distance and the correlation coefficient of solar irradiance is similar; When the geographical distance is 5 km, the correlation coefficient of photovoltaic output drops to 0.75, which may have a strong impact on the distribution network power flow and MHC;

[0072] To further reveal the relationship between correlation and distance and the modeled correlation under any network configuration, equation (14) is used to fit the photovoltaic output data as:

[0073]

[0074] Equation (15) is an exponential decay formula, which conforms to the empirical relationship between the clear sky index and spatial distance;

[0075] Through the test of actual example data in a certain city area, it is proved that the probability modeling method of distributed photovoltaic output considering spatial correlation based on the Copula algorithm proposed by the present invention can accurately simulate the actual output curve of distributed photovoltaic power stations, and is basically consistent with the trend of the empirical relationship curve between spatial distance and output in typical areas.

[0076] Inspired by the above ideal embodiments of the present invention, through the above description, relevant staff can make various changes and modifications completely within the scope of not deviating from the technical idea of this invention. The technical scope of this invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for probabilistic modeling of spatially correlated output of distributed photovoltaic Characterized in that, Comprising the following steps: S1. Determine the empirical correlation between the clear sky indices at N locations to obtain a correlation matrix P; The step of determining the empirical correlation between the clear sky indices at N locations to obtain a correlation matrix P includes: S11. Define the ratio of the horizontal surface irradiance G i (t) at site i to the horizontal surface clear-sky irradiance G c，i (t) at the same site at time t; i (t) and the horizontal surface clear-sky irradiance G c，i (t) at the same site at time t; S12. Take the instantaneous clear sky index of each site as the random variable X i ; At a given site and time, the probability distribution of solar irradiance is denoted by X i G c，i (t), where G c，i (t) gives the scalar value of the determined clear-sky irradiance at time t; S13. Model using the Pearson correlation coefficient according to the correlation between pairs of random variables: Among them, Cov(X i , X j ) is the covariance of X i and X j , and σ i , σ j are the corresponding standard deviations; S14. Represent the overall correlation structure between all pairs of sites with a correlation matrix: When modeling the correlation for any network configuration, use the exponential decay model of the pair-site correlation: ρ(Δx) = e -γΔx (5) Where γ is a parameter that determines how fast the correlation decays with distance, and Δx is the distance between two sites; S2. Define a multivariate Gaussian distribution N(μ, P) using the correlation matrix, where μ = [μ 1 ,..., μ N , and μ i ≡ 0; The step of using the correlation matrix to define the multivariate Gaussian distribution N(μ, P) includes: S21. Establish a random variable and the X distribution; Randomly draw a number u from the distribution of U, and a sample of the X distribution obtained is: Vice versa, that is, the random variable has a uniform distribution, so when inputting x from the distribution of X to the resulting distribution of u is uniform; S22. Obtain from the sample x 1 ,..., x n , where the uniform distribution values u corresponding to all samples 1 ,..., u N all have their respective correlations; S3. Extract samples v from the multivariate Gaussian distribution 1 ,..., v N ; S4. Obtain the relevant uniform distribution value u from the one - variable Gaussian cumulative distribution function i = Φ(v i ), i = 1,..., N; S5. Obtain relevant samples from the distribution of the clear sky index S6. Convert the clear sky index into the photovoltaic power injected into the distribution network bus, and establish a probabilistic model of distributed photovoltaic output considering spatial correlation according to the output data of grid-connected distributed photovoltaic power plants; The conversion of the clear sky index into the photovoltaic power injected into the distribution network bus is achieved by calculating the DC power output of the photovoltaic array on the inclined plane, and the DC power output is: P dc = AG T η(1 - q a ) (12) Wherein, A is the total area of the photovoltaic array; η is the conversion efficiency of the photovoltaic module; q a is the additional loss rate; The AC power output by the photovoltaic system inverter is determined based on the Sandia inverter model: P ac0 is the rated maximum AC power of the inverter; P dc0 is the DC power when the inverter reaches the AC rated power; P s0 is the threshold power of the inverter.

Images