A power distribution network accommodation capacity evaluation method based on extreme value theory

Abstract

The application discloses a kind of based on extreme value theory's distribution network consumption capacity evaluation method, first, extreme value theory is used to carry out fluctuating load modeling, determine distribution network line and distribution network fluctuating load recurrence period and recurrence level;Second, extreme value distribution is used to fit the tail distribution of node injection power, calculate T year line maximum load rate, to quantify line flow and the load capacity of distribution line under different overrun probability;Finally, according to the actual load type of distribution network, the feeder load rate under multiple types of load is calculated as the load evaluation index of distribution network line, to evaluate its distributed power consumption capacity.The application can obtain the line load rate level under different recurrence period and the recurrence period under the proposed line limit load rate;Therefore, the fluctuating load consumption capacity of line can be evaluated in time, and theoretical basis is provided for the future distribution network planning with high proportion of fluctuating load access.

Description

TECHNICAL FIELD

[0001] The application relates to a power distribution network accommodation capacity evaluation method, in particular to a power distribution network distributed power accommodation capacity evaluation method suitable for high-proportion renewable energy access. BACKGROUND

[0002] The accommodation capacity of the power distribution network is mainly affected by the net load of the injection node and ultimately depends on the two safety constraints of the power distribution line capacity and the node voltage. In the ADN framework, the voltage in the power distribution network can be adjusted by OLTC, SVC, CB and other devices, and only in rural distribution networks with weak adjustment capacity and large distribution line impedance. In most power distribution networks, the relationship between the node net load and the distribution line capacity determines the accommodation capacity of the distribution line, more accurately, the relationship between the extreme value distribution of the line flow and the distribution line capacity determines the accommodation capacity of the distribution line.

[0003] The traditional method of studying the relationship between the line flow extreme value distribution and the distribution line capacity is to calculate the probability distribution of the line flow by the probability flow algorithm and then intercept the tail of the distribution. However, this method is time-consuming and data-consuming, and there is a lot of data waste in the calculation process. At present, the power distribution network is developing in the direction of gradually increasing proportion of distributed power and renewable energy, and the conventional method is no longer applicable. SUMMARY

[0004] The application aims to provide a power distribution network distributed power accommodation capacity evaluation method suitable for high-proportion renewable energy access.

[0005] Technical scheme: The power distribution network accommodation capacity evaluation method based on the extreme value theory comprises the following steps:

[0006] (1) The fluctuating load is modeled by using the extreme value theory to determine the recurrence period and the recurrence level of the fluctuating load in the power distribution network line;

[0007] (2) The tail distribution of the node injection power is fitted by using the extreme value distribution, and the maximum load rate of the line in T years is calculated to quantify the line flow and the load capacity of the distribution line under different exceeding probabilities;

[0008] (3) The feeder load rate under multiple types of loads is calculated according to the actual load type of the power distribution network as a load evaluation index of the power distribution network line, and the distributed power accommodation capacity is evaluated.

[0009] The load recurrence period in the step (1) is the time interval of the maximum load; the load recurrence level is the maximum load on the line L in the recurrence period T, denoted as X p = 1 / T.

[0010] The load recurrence level is calculated according to the following formula:

[0011]

[0012] The extreme value distribution of the line load is expressed by a GEV distribution in the step (2), and the CDF is H(x|μ,σ,ξ), and the line load rate corresponding to the T-year recurrence period is expressed as:

[0013]

[0014] In the formula, P max is the maximum load of the line; S max is the line capacity.

[0015] The ratio of the maximum value of the load of the line occurring in the T-year period to the maximum power transmission capacity of the line is defined as the T-year line maximum load rate, that is:

[0016]

[0017] In the formula, δ is the load growth rate, indicating the load growth speed of the line in the T-year period, and is calculated according to the following formula:

[0018]

[0019] In the formula, represents the load size of the line in the T time interval.

[0020] The load types in the step (3) include park industrial load, park commercial load, park residential load, urban industrial load, urban commercial load, urban residential load and rural residential load.

[0021] The step (3) includes the following steps:

[0022] (31) initializing the power distribution network load sample data to obtain daily extreme value sample sequences of different types of loads;

[0023] (32) fitting the GEV distribution function of the daily extreme value of each type of load, and calculating the load recurrence level;

[0024] (33) calculating the load simultaneous rate, and solving the T-year line maximum load rate;

[0025] (34) estimating the line load state recurrence period.

[0026] In the step (31), when the number of load types with typical load use characteristics in the line is N, the annual load sample unit value [P1, P2,..., P 8760As sample data, the annual load data is divided into 365 intervals with daily load data as single interval, the number of single-day load sample is 24, and the daily load maximum value of the mth day and jth type load is expressed as follows:

[0027] X m = max(P i ), i ∈ {24(m-1), 42(m-1)+1, …, 24m}

[0028] The daily extreme value sample sequence of N types of loads is obtained by initializing each type of load sample.

[0029] In the step (32), the daily load extreme value of single type of electricity consumption load can be approximately regarded as an independent and identically distributed random variable, and according to Fisher-Tippet extreme value type theorem, it is assumed that the extreme value of single type of load daily interval constitutes a sequence satisfying GEV distribution; according to the sample sequence {X1, X2, …, X 365}, the GEV distribution function H(x: μ, σ, ξ) of each type of load daily maximum value is estimated by maximum likelihood estimation method;

[0030] After obtaining the GEV parameters of each type of load, the corresponding recurrence level X p of each type of load corresponding to the recurrence period T is calculated.

[0031] In the step (33), the load simultaneous rate is the ratio of the daily peak value of the total load of the line and the sum of the daily peak values of each load point, the load groups are divided according to the user load type, and the daily characteristic curve of the typical load point in each load group is selected to approximately calculate the load simultaneous rate as follows:

[0032]

[0033] In the above formula, P e,j is the size of j type group load, which is a named value; P t,j is the daily load peak value of j type group load, which is a unit value;

[0034] The T-year period line maximum load rate of the line containing multiple types of loads is calculated as follows:

[0035]

[0036] In the above formula, the load maximum value of the line in the T period is calculated as follows:

[0037]

[0038] P p.j is the size of j type group load in T period, which is calculated as follows:

[0039]

[0040] In the above formula, P e,j is the j-type group load size, which is a named value.

[0041] In step (33), the line maximum load rate exceeds the line optimal load rate η hl once every T time interval, and the event is considered to occur once a line overload event. hl The line limit load rate exceeds η ol once every T time interval, and the event is considered to occur once a line overload event. ol The minimum recurrence period of the corresponding line overload event and overload event is calculated according to the following formula:

[0042]

[0043] In the formula, f --1 represents the inverse function of f in formula (14); p hl and p ol are the probabilities of the line overload event and the overload event, respectively.

[0044] Advantages: Compared with the prior art, the present application has the following significant advantages: calculating the feeder limit load rate from historical sample data can obtain the line load rate level under different recurrence periods such as "once a year", "once every five years" and "once every ten years"; the line limit load rate index can estimate the recurrence period corresponding to different load rate levels of the line, and can timely evaluate the fluctuating load accommodation capacity of the line. It can evaluate the accommodation capacity of the distribution network according to the relationship between the line flow extreme value distribution and the capacity of the distribution line, not only can provide guidance for evaluating the accommodation capacity of the distribution network for distributed power, but also can provide support for the future planning of the distribution network with high proportion of fluctuating load, and promote the active and orderly development of new energy industry. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 is a flowchart of the present application;

[0046] Figure 2 The distribution network system of the three embodiments (a), (b) and (c) of the present application;

[0047] Figure 3 is the load annual time series curve of the three embodiments of the present application;

[0048] Figure 4 is the GEV distribution fitting histogram of the load of the three embodiments of the present application;

[0049] Figure 5 is the P-P diagram of the load of the three embodiments of the present application;

[0050] Figure 6 These are load reproducibility level variation curves for three embodiments of the present invention;

[0051] Figure 7 These are the line limit load rate curves for three embodiments of the present invention. Detailed Implementation

[0052] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0053] Let X1, X2, ..., X n Let x be a set of independent and identically distributed random variables with a common cumulative distribution function (CDF) H(x), and define the maximum sample value M. n =max(X1,X2,…,X) n If there exists a constant column {a} n >0} and {b n If equation (1) holds, then H must belong to one of the three basic distribution types, and H is called the generalized extreme value (GEV) distribution. The asymptotic distribution of the sample extreme value x obtained from GEV has a CDF as shown in equation (2).

[0054]

[0055] Pr(M n ) = Pr(X1,…,X n )

[0056] Pr(X1,…,X n )=H(x:μ,σ,ξ)

[0057]

[0058] Mn≤x,X1≤x,…,X n ≤x (2)

[0059] In the formula, the domain of the random variable x is 1+ξ(x-μ) / σ>0; μ is the location parameter, representing the "center" of the distribution; σ is the scale parameter, used to control the magnitude of the deviation relative to μ; and ξ is the shape parameter.

[0060] Correspondingly, the PDF of the random variable X is shown in equation (3).

[0061]

[0062] Return periods and return levels are often used in fields such as environment, architecture, finance, and hydrology to quantify the risk tolerance of actual projects. Generally speaking, the m-year return level X of a random variable means that the random variable reaches the value of X once every m years on average, that is, the probability that the maximum value of the random variable exceeds X is 1 / m.

[0063] When the cumulative distribution function H(x) of the random variable x follows a GEV distribution, in order to describe the tolerance of actual projects to extreme low-probability events caused by extreme value fluctuations of the variable x, the quantile regression method is often used to estimate the return level X of the sample extreme value at the p (0 < p < 1) quantile of H(x|μ, σ, ξ). p , and its expression is as follows:

[0064] X p = inf{x|H(x)}, H(x) ≥ p (4)

[0065] Combined with Equation (2), the return level defined by the quantile function can be calculated using Equation (5):

[0066] X p = H -1 (p)

[0067]

[0068] In the formula, the x value corresponding to the extreme value quantile is used as the return level of extreme events; T = 1 / p is the return period, which is defined as an extreme value event of size X occurs once every T time intervals, and the return period and return level correspond one by one. p As shown, in this invention, extreme value theory is used to model the volatile load, the concepts of the return period and return level of the volatile load are introduced, and the maximum load rate in the distribution network line is calculated; the tail distribution of the node injection power is fitted using the extreme value distribution to further quantify the line power flow and the load capacity of the distribution line under different over-limit probabilities; and a method for calculating the feeder load rate applicable to multi-type load scenarios is proposed as an evaluation index for the distribution network line load, further providing guidance for the assessment of the distributed power consumption capacity of the distribution network. The specific steps include:

[0069] Such as Figure 1 shown, in this invention, extreme value theory is used to model the volatile load, the concepts of the return period and return level of the volatile load are introduced, and the maximum load rate in the distribution network line is calculated; the tail distribution of the node injection power is fitted using the extreme value distribution to further quantify the line power flow and the load capacity of the distribution line under different over-limit probabilities; and a method for calculating the feeder load rate applicable to multi-type load scenarios is proposed as an evaluation index for the distribution network line load, further providing guidance for the assessment of the distributed power consumption capacity of the distribution network. The specific steps include:

[0070] (1) Use extreme value theory to model the volatile load and determine the return period and return level of the volatile load in the distribution network line;

[0071] (2) Use the extreme value distribution to fit the tail distribution of the node injection power and calculate the maximum load rate of the line in the T-year period to quantify the line power flow and the load capacity of the distribution line under different over-limit probabilities;

[0072] (3) Calculate the feeder load rate under multiple types of loads based on the actual load type of the distribution network as the load evaluation index of the distribution network line to evaluate its distributed power absorption capacity.

[0073] In step (1), the load recurrence level is defined as the maximum load on line L within the recurrence period T, denoted as X. p =1 / T. The calculation of load recurrence level is the same as formula (5).

[0074] In step (2), assuming the extreme value distribution of the line load can be represented by the GEV distribution, and its CDF is H(x|μ,σ,ξ), then the line load factor corresponding to the T return period can be expressed as:

[0075]

[0076] In the formula, P max S represents the maximum load of the line. max This refers to the line capacity.

[0077] Furthermore, the ratio of the maximum load value of the line within the return period T to the maximum transmission capacity of the line is defined as the maximum load factor of the line in year T (hereinafter referred to as the maximum load factor in year T), that is:

[0078] η T =f(p)

[0079]

[0080] Considering the growth of line load within the planned area, let the load growth rate be δ, representing the rate of load growth of the line within the return period T:

[0081]

[0082] In the formula, This indicates the load on the line during the T-th time interval.

[0083] Compared to traditional deterministic indicators based on maximum values, the T-year maximum load factor assesses the load status of distribution network lines based on historical line loads. This not only provides probabilistic information on line load status but also reveals the trend of load status changes with load growth. By specifying different return periods and return levels, the T-year maximum load factor can quantify line power flow and the load capacity of distribution lines under different over-limit probabilities using the following application methods:

[0084] (1) Obtain the line limit load rate recurrence level under each return period. By calculating the feeder limit load rate through historical sample data, the line load rate level under different return periods such as "once a year", "once a five-year period" and "once a ten-year period" can be obtained.

[0085] (2) Obtain the return period under the proposed line limit load rate. The return period corresponding to different load rate levels of the line can be estimated by using the line limit load rate index, so as to provide timely guidance on the line's ability to absorb fluctuating loads.

[0086] Step (3) includes the following steps:

[0087] (31) Sample data initialization

[0088] In order to minimize the required data sample size while maintaining the accuracy of load extreme value distribution, the present invention initializes annual sample data for different types of loads (such as residential loads, commercial loads, industrial loads, etc.) in the distribution network.

[0089] When the number of load types with typical load characteristics (such as industrial load, commercial load, residential load, and agricultural load) in the line is N, extract the per-unit values ​​of the annual load samples of typical load points among the j-th type of load users [P1, P2, ..., P]. 8760 The minimum precision of the sample is on the hourly level. Dividing the annual load data into 365 intervals using daily load data as a single interval, the number of daily load samples is 24. Furthermore, the daily load maximum of the j-th type of load on the m-th day can be expressed as follows:

[0090] X m =max(P i ),i∈{24(m-1),42(m-1)+1,…,24m} (9)

[0091] By initializing the load samples of each type, we can obtain the daily extreme value sample sequence of N types of loads.

[0092] (32) Fit the GEV distribution function of the daily maximum value of each type of load and calculate the load recurrence level.

[0093] By initializing with sample data, the daily extreme values ​​of a single type of electricity load can be approximated as independent and identically distributed random variables. Therefore, according to the Fisher-Tippet extreme value type theorem, it can be assumed that the sequence of extreme values ​​for a single type of load within a daily interval satisfies a GEV distribution. Due to the excellent properties of the unbiased and asymptotically normal nature of the maximum likelihood estimation method, based on the sample sequence of daily load extreme values ​​{X1, X2, ..., X...}, 365 The GEV distribution function H(x:μ,σ,ξ) of the daily maximum value of each type of load is estimated using the maximum likelihood estimation method.

[0094] Once the parameters of the GEV for each type of load are obtained, the recurrence level X corresponding to the recurrence period T for each type of load can be calculated using equation (5). p .

[0095] (33) Calculate the load simultaneity rate and solve for the maximum line load rate in year T.

[0096] The load simultaneity rate is an important parameter characterizing the load characteristics of a power system. It is used to describe the temporal differences in the occurrence of peak loads of various types within a sample period. It is defined as the ratio of the daily peak load of the total line load to the sum of the daily peak loads of each load point.

[0097]

[0098] Where L is the number of loads in the feeder; P t,i Let i be the load value of load i at time t (t = 1, 2, ..., n) within the daily interval.

[0099] By dividing the load into groups based on user load type and selecting the daily characteristic curves of typical load points in each load group, the load simultaneity rate can be approximated as follows:

[0100]

[0101] In the formula, P e,j P represents the load size for group j, a named value. t,j Let be the daily peak load of type j group, and be a per-unit value.

[0102] Due to differences in economic development levels and load types within the distribution network's region, the load growth rates for different load types vary under different scenarios, generally ranging from 5% to 10%. Therefore, the growth rate of each load type should be considered separately. To simplify calculations, this paper approximates the daily average of the annual load growth rate with the daily load growth rate. The maximum load on the line during period T can then be expressed as:

[0103]

[0104] In the formula, P p.j The load size of group j within time period T is calculated as follows:

[0105]

[0106] Substituting equations (10), (11), (12), and (13) into (8), we can obtain the maximum load factor of the line with multiple types of loads in year T as follows:

[0107] η T =f(p)

[0108]

[0109] (34) Estimating the return period of line load conditions

[0110] Due to differences in distribution network connections, the optimal load factor for each line also varies. (In terms of per ton) hl The maximum load rate of the line exceeds the optimal load rate η once at intervals. hl An event is considered a line overload event, with each T ol The line's maximum load rate exceeds η once every time interval. ol An event is considered an overload event. The minimum return period for the corresponding heavy load and overload events can be calculated as shown in equation (15):

[0111]

[0112] In the formula, f --1 The inverse function of f in expression (14); p hl and p ol These represent the probabilities of a line experiencing a heavy load event and an overload event, respectively.

[0113] In the specific implementation process, based on the typical calculation examples in the "National Key Research and Development Program Project (2016YFB0900100)", we selected 10kV actual distribution networks under three different load scenarios in my country, namely a rural area in Anhui, an urban area in Zhejiang, and an industrial park in Jiangsu, as specific implementation examples. We evaluated the absorption capacity according to the method described in this invention and verified its effectiveness and accuracy.

[0114] Example 1: Industrial Park Scenario: The power distribution network includes 37 nodes, 2 substations, and 2 feeders, with a load capacity of 29.48MW;

[0115] Example 2: Urban Scenario: The power distribution network includes 45 nodes, 3 substations, and 5 feeders, with a load capacity of 18.124MW;

[0116] Example 3: Rural scenario: The power distribution network includes 51 nodes, 1 substation, 3 feeders, and a load capacity of 6.875MW.

[0117] The distribution network topology corresponding to each embodiment is as follows: Figure 2 As shown in Table 1, the line data and their maximum transmission capacity are listed below.

[0118] Table 1. Line data for three power distribution systems

[0119]

[0120]

[0121] Based on actual distribution network load data, annual load curves for typical loads such as industrial load, commercial load, and residential load in three scenarios in 2016 are selected as follows: Figure 3The sample time interval was 1 hour, and the total number of samples collected throughout the year for each type of load was 8760. The load sizes of different types of loads on each line under the three load scenarios are shown in Table 2.

[0122] Table 2 Various loads on the line

[0123]

[0124] Typical daily load characteristic curves for various scenarios are as follows: Figure 4 Among them, the residential load is lower at noon and at night, which is in line with the residents' work and rest patterns; the commercial load has a longer working time during the day, but still has a large load fluctuation at night; the industrial load is relatively stable during working hours, with a longer load peak; the agricultural load has similar characteristics to the residential load, but the overall load peak occurs earlier; the electric vehicle load fluctuates greatly, and the load peak generally occurs at night and during the midday commute.

[0125] Data initialization was performed on the annual hourly data series of loads for industrial load, commercial load, residential load, urban industrial load, urban commercial load, urban residential load, and rural residential load. The parameters of the load GEV distribution under each scenario were obtained by using the maximum likelihood estimation method, as shown in Table 3.

[0126] Table 3. GEV distribution parameters of load under different scenarios

[0127]

[0128]

[0129] Table 3 shows that, comparing the GEV distribution parameters of different load types in the same scenario, the shape parameter ξ of residential and commercial loads is >0, exhibiting a Fréchet distribution with a fat-tailed tail, and the location parameter μ is concentrated around 0.3–0.4; the industrial load is <0, exhibiting a Weibull distribution with a truncated tail, and the location parameter is concentrated between 0.3 and 0.6. Comparing the GEV distribution parameters of the same load type in different scenarios, in the park scenario, industrial load is the main load, and its location parameter μ is relatively high; the scale parameter σ of residential load is small, and the load extreme values ​​are more concentrated, because the working hours of residents in the park scenario are relatively regular; in the urban scenario, the scale parameter σ of the extreme value distribution of each load type is higher than in other scenarios, because urban areas have diverse user load types and load peaks are easily affected by factors such as holidays and weather; in the rural scenario, due to fewer load types and a higher proportion of residential load, the location parameter μ is larger, and the load extreme values ​​are relatively larger.

[0130] Histograms and PP charts in the above three scenarios are as follows: Figure 4 andFigure 5 As shown, the fitted curve of the GEV extreme value distribution is very close to the histogram, and the PP plot is approximately a straight line, so the fitting can be considered to be in line with expectations.

[0131] In addition, the reproducibility levels X of the three load types in the three scenarios p The curve showing the change with p is shown below. Figure 6 .Depend on Figure 6 It can be seen that the extreme values ​​X of each type of load p As the p-value increases, it gradually decreases. The reproducibility curves of the same load type under different scenarios show similar trends, proving the rationality of fitting the GEV function based on the load type.

[0132] Combination Figure 6 As can be seen from Table 3, the reproducibility level curves of the same type of load differ in different scenarios. p The height at p=1 is determined by the position parameter μ, X p The rate of change with p is determined by both the shape parameter ξ and the scale parameter σ. The GEV of industrial load follows a Weibull distribution, exhibiting a truncated characteristic, and its X... p The curve showing the change of p value intersects the vertical axis. As the p value decreases, the load reproducibility level X compared to other types of loads... p The changing trend is relatively gentle; the GEV of residential and commercial loads follows a Fréchet distribution, exhibiting fat-tailed characteristics, with X showing a relatively flat trend at low p-values. p The changing trend is obvious. Therefore, compared with industrial load, commercial load and residential load have a higher load recurrence level when the p-value is small, that is, when the return period is long.

[0133] Next, when calculating the maximum load factor of each line in year T under the three scenarios, the following assumptions are made:

[0134] (1) In order to describe the impact of the differences in regional economic development level and power development demand on the line limit load rate, the annual load growth rate in scenarios such as rural areas, industrial parks and urban areas is set to 5%, 7% and 10%, respectively.

[0135] (2) The load capacity of EV and agricultural load in the example is relatively small, making it difficult to obtain load output data over a long time scale. Therefore, when calculating the extreme load factor, X p All are approximated by the peak load of a typical day.

[0136] (3) Based on the wiring method of the distribution network in different scenarios, under the N-1 criterion, according to Table 4, the optimal load rate of the distribution network system line in the industrial park scenario can be set to 50%, and the optimal load rate of the distribution network system line in the urban scenario can be set to 75%. In particular, since the rural scenario is a single radial network, it does not meet the N-1 criterion, and only the overload event when the limit load rate exceeds 100% is considered.

[0137] The optimal load factor for each medium-voltage distribution network line under the N-1 criterion is shown in Table 4:

[0138] Table 4 Optimal Load Rate of Power Distribution Lines

[0139]

[0140] The calculation results for the three test systems obtained through equations (10) and (11) are shown in Table 5, where λ is the line load simultaneity rate; η is the line traditional load rate; η t T represents the maximum load factor of the line during its return period of t years; hl T represents the minimum return period at which the line's maximum load rate exceeds its optimal load rate as the return period increases; the unit is days (d). ol This represents the minimum return period when the line's ultimate load factor first exceeds 1, expressed in days (d). The curve showing the change in the line's ultimate load factor from 0 to 1.4 as the return period T varies is shown below. Figure 7 As shown.

[0141] Since the traditional line load rate only reflects the line load status within the sample statistical period, comparing the "once-a-year" limit load rate η1 of each line in Table 4 with the traditional line load rate η shows that η1 and η are very close for each line in the industrial park and urban scenarios, proving the accuracy of the limit load rate indicator. In the rural scenario, η1 and η differ significantly. This is because the rural scenario in the calculation only considers two load types: residential load and agricultural load. Furthermore, agricultural load does not have a year-round output curve, resulting in a larger error when the return period is short.

[0142] Table 5. Calculation results of line load rate under different scenarios

[0143]

[0144] Combination Figure 7 As shown in Table 5, the feeder limit load rate variation curves under the same scenario may intersect. This indicates that, influenced by the electricity consumption characteristics of different types of load users, lines with lower limit load rates in the short-term return period may have higher rates in the long-term return period. For example, in the urban scenario, η1 of feeder II is lower than that of feeder III, while η5 and η 10On the contrary, it is relatively high. This result indicates that the trend of line load rate changes is not the same due to the influence of line load structure and power consumption characteristics. Therefore, compared with the traditional static load rate, studying the maximum line load rate within different return periods can reflect the trend of line load rate changes to a certain extent, and is more conducive to accurately measuring the risk of line load exceeding limits.

[0145] Comparison of the heavy load return period T of different feeders hl and overload return period T ol It can be seen that, in the same scenario, different lines have different load capacities due to their varying power consumption characteristics, resulting in different return periods for heavy load and overload states. When the return period reaches a certain value, the return level of the ultimate load rate for each line is approximately linearly related to the return period. Based on this, comparing two lines with the same maximum transmission capacity in the same scenario, such as Line II and Line III in an urban scenario, it can be observed that when the industrial load content, exhibiting a Fréchet distribution in the GEV distribution, is high, the slope of its ultimate load rate return level curve is lower, consistent with... Figure 6 The results demonstrate that the line limit load rate index can reflect the differences in line load status changes under the same load scenario with different load densities. It has significant advantages in assessing the load status of lines containing various fluctuating loads.

Claims

1. A method for evaluating the absorption capacity of a distribution network based on extreme value theory, characterized in that, Includes the following steps: (1) Use extreme value theory to model fluctuating loads and determine the recurrence period and recurrence level of fluctuating loads in the distribution network lines; (2) The tail distribution of the injected power at the nodes is fitted by the extreme value distribution to calculate the maximum load rate of the line in year T, so as to quantify the power flow and the load capacity of the distribution line under different over-limit probabilities. Includes the following steps: (21) Obtain the line limit load rate recurrence level under each recurrence period, and calculate the feeder limit load rate through historical sample data to obtain the line load rate level under different recurrence periods. (22) Obtain the return period under the proposed line limit load rate, and estimate the return period corresponding to different load rate levels of the line through the line limit load rate index. (3) Calculate the feeder load rate under multiple types of loads based on the actual load type of the distribution network as the distribution network line load evaluation index to assess its distributed power absorption capacity. Includes the following steps: (31) Initialize the load sample data of the distribution network to obtain the daily extreme value sample sequence of different types of loads; (32) Fit the GEV distribution function of the daily maximum value of each type of load and calculate the load recurrence level; (33) Calculate the load simultaneity rate and solve for the maximum line load rate in year T; (34) Estimate the recurrence period of line load conditions; The load types include industrial load in the park, commercial load in the park, residential load in the park, industrial load in the city, commercial load in the city, residential load in the city, and residential load in the countryside.

2. The method for evaluating the absorption capacity of a distribution network based on extreme value theory according to claim 1, characterized in that, The load recurrence period in step (1) is the time interval between the occurrence of the maximum load; the load recurrence level is the maximum load on line L within the recurrence period T, denoted as X. p =1 / T; The load recurrence level is calculated using the following formula:

3. The method for evaluating the absorption capacity of a distribution network based on extreme value theory according to claim 1, characterized in that, In step (2), the extreme value distribution of the line load is represented by the GEV distribution, and its CDF is H(x|μ,σ,ξ). The line load rate corresponding to the T return period is expressed as: In the formula, P max This represents the maximum load on the line. S max For line capacity, The maximum load factor of a line during its return period T is defined as the ratio of the maximum load value within that period to the line's maximum transmission capacity. In the formula, δ represents the load growth rate, indicating the rate of load increase of the line within the return period T, and is calculated using the following formula: In the formula, This indicates the load on the line during the T-th time interval.

4. The method for evaluating the absorption capacity of a distribution network based on extreme value theory according to claim 1, characterized in that, In step (31), when the number of load types with typical load characteristics in the line is N, the per-unit values ​​of the annual load samples of typical load points in the j-th type of load user are extracted [P1, P2, ..., P]. 8760 As sample data, the annual load data is divided into 365 intervals, with daily load data as a single interval. The number of daily load samples is 24. The daily load maximum value of the j-th type of load on the m-th day is expressed as follows: X m =max(P i ),i∈{24(m-1),42(m-1)+1,…,24m} The daily extreme value sample sequence of N types of load is obtained by initializing the load samples of each type.

5. The method for evaluating the absorption capacity of a distribution network based on extreme value theory according to claim 1, characterized in that, In step (32), the daily extreme values ​​of a single type of electricity load can be approximated as independent and identically distributed random variables. Based on the Fisher-Tippet extreme value type theorem, it is assumed that the sequence of extreme values ​​in the daily intervals of a single type of load satisfies a GEV distribution. Based on the daily maximum value sample sequence {X1,X2,...,X...} 365 The GEV distribution function H(x:μ,σ,ξ) of the daily maximum value of each type of load is estimated using the maximum likelihood estimation method. After obtaining the parameters of GEV for each type of load, calculate the recurrence level X corresponding to the recurrence period T for each type of load. p .

6. The method for evaluating the absorption capacity of a distribution network based on extreme value theory according to claim 1, characterized in that, In step (33), the load simultaneity rate is the ratio of the daily peak value of the total line load to the sum of the daily peak values ​​of the loads at each load point. Load groups are divided according to user load type, and the daily characteristic curves of typical load points in each load group are selected. The load simultaneity rate is then approximated as follows: In the above formula, P e,j P represents the load size for group j, which is a named value. t,j The daily peak load for load group j is a per-unit value. The maximum load factor of a line containing multiple types of loads in year T is calculated using the following formula: In the above formula, the maximum load of the line during time period T is calculated using the following formula: P p.j The load size of group j within time period T is calculated as follows: In the above formula, P e,j This represents the load size for group j, and is a named value.

7. The method for evaluating the absorption capacity of a distribution network based on extreme value theory according to claim 1, characterized in that, In step (33), per T hl The maximum load rate of the line exceeds the optimal load rate η once at intervals. hl An event is considered a line overload event, with each T ol The line's maximum load rate exceeds η once every time interval. ol An event is considered an overload event, and the minimum return period for the corresponding heavy load and overload events is calculated using the following formula: In the formula, f --1 The inverse function of f in expression (14); p hl and p ol These represent the probabilities of a line experiencing a heavy load event and an overload event, respectively.

Images