A power distribution network risk assessment method based on photovoltaic output prediction error

Abstract

The application discloses a power distribution network risk assessment method based on photovoltaic output prediction error, constructs an isolated tree of an isolated forest algorithm, carries out fusion processing on massive distributed photovoltaic output historical data, and corrects abnormal values of photovoltaic output; based on a photovoltaic output typical scene, a probability distribution model of photovoltaic output prediction error is constructed, wherein based on an adaptive K-means clustering algorithm, a power distribution network photovoltaic typical output scene is divided, according to meteorological conditions, BiLSTM is adopted to perform ultra-short-time prediction on distributed photovoltaic output, a photovoltaic output prediction curve is obtained, KDE is adopted to model photovoltaic output prediction error, and a probability distribution curve of photovoltaic output prediction error is obtained; in combination with a semi-invariant and a Gram-Charher expansion series method, the probability distribution of node voltages of the power distribution network is obtained through probability power flow calculation; the node voltage out-of-limit probability of the power distribution network is calculated, and the voltage out-of-limit risk of the power distribution network is evaluated. The application can determine key uncertainty factors in the change of the operation state of the power distribution network.

Description

Technical Field

[0001] This invention relates to the field of power system risk assessment, and specifically to a method for risk assessment of distribution networks based on photovoltaic output prediction errors. Background Technology

[0002] Guided by the "dual carbon" goals, my country is actively promoting the construction of a new power system with new energy sources as the mainstay, vigorously developing distributed new energy, and the high proportion of distributed power sources connected to the distribution network has gradually become a key feature of the future power system. However, the power output of photovoltaic power generation has obvious randomness and volatility, mainly affected by factors such as weather conditions and solar radiation intensity. This uncertainty makes the prediction error of photovoltaic power generation a significant challenge in the operation of the distribution network.

[0003] Existing risk assessment methods for distribution networks typically rely on historical data and traditional load forecasting models, failing to adequately consider the impact of photovoltaic (PV) power output forecasting errors on the stability and security of the distribution network. Therefore, with the gradual increase in PV power generation systems, traditional risk assessment methods often struggle to accurately assess the risks of the distribution network in actual operation. This can lead to severe power supply problems or equipment overload during PV power fluctuations, thereby affecting the safe and stable operation of the power system. Furthermore, while existing PV power forecasting technologies have made some progress, they still suffer from low forecasting accuracy and large error fluctuations. These problems have not been effectively addressed in distribution network risk assessment, resulting in inaccurate assessments of the actual operational risks of the distribution network. Therefore, a new method is urgently needed to comprehensively consider PV power output forecasting errors to more accurately assess the risks of the distribution network, thereby improving its stability and reliability. Summary of the Invention

[0004] The purpose of this invention is to provide a distribution network risk assessment method based on photovoltaic power output prediction error, so as to ensure the accuracy of voltage risk assessment of the distribution network when photovoltaic power output prediction error disturbance occurs and to shorten the risk assessment time as much as possible.

[0005] The technical solution to achieve the purpose of this invention is: a distribution network risk assessment method based on photovoltaic power output prediction error, comprising the following steps:

[0006] Step 1: Construct isolated trees for the isolated forest algorithm, fuse massive historical data of distributed photovoltaic power output, and correct outliers in photovoltaic power output;

[0007] Step 2: Based on typical photovoltaic power output scenarios, construct a probability distribution model for photovoltaic power output prediction errors. This involves using an adaptive K-means clustering algorithm to segment typical photovoltaic power output scenarios in the distribution network, using BiLSTM to perform ultra-short-time prediction of distributed photovoltaic power output based on meteorological conditions to obtain the photovoltaic power output prediction curve, and using KDE to model the photovoltaic power output prediction error to obtain the probability distribution curve of the photovoltaic power output prediction error.

[0008] Step 3: Combining the semi-invariant and Gram-Charlier series expansion methods, the probability distribution of voltage at each node of the distribution network is obtained through probabilistic power flow calculation, including the node voltage probability density curve and probability distribution curve, to describe the uncertainty of the system in the form of probability distribution.

[0009] Step 4: Calculate the probability of voltage exceeding the limit at the nodes of the distribution network and assess the risk of voltage exceeding the limit in the distribution network.

[0010] Furthermore, in step 1, the historical data of massive distributed photovoltaic power output is fused and processed to correct outliers in photovoltaic power output. The specific method is as follows:

[0011] Step 1.1: Construct the isolation tree of the isolation forest algorithm, and isolate the abnormal photovoltaic power output data points by gradually splitting the data points;

[0012] First, randomly select n sample data points from the massive photovoltaic power output data as a subset and construct an initial iTree, placing the subset into the root node of the tree. Then, randomly specify an attribute dimension q from multiple dimensions of the data and randomly generate a cutting point p in the current node's data. Subsequently, generate a hyperplane at this cutting point to divide the current node's data space into two subspaces. Place data items with attribute values ​​less than p into the left subspace of the current node; otherwise, place them into the right subspace. Repeat the above steps recursively until the subspaces can no longer be cut or the iTree has reached its limit height.

[0013] Step 1.2: Calculate the isolated path length of each output data point in the isolated forest and obtain the corresponding anomaly score to detect abnormal data points;

[0014] For test data x, substitute it into each iTree in the forest, calculate the depth h(x) where it falls on each tree, and calculate the average of all h(x) as E(h(x)). Combine the standard average search length l(n) and the harmonic number H(x) to calculate the anomaly score of the test data.

[0015] Set the standard average search length l(n) and harmonic number H(x) as follows: l(n)=2H(n-1)-[2(n-1) / n] (1)

[0016] H(i)=ln(i)+0.5772 (2)

[0017] The anomaly score for the data to be tested is:

[0018]

[0019] If u(x,n) is close to 1, the data is considered to be abnormal. For abnormal data, the nearest neighbor interpolation method is used for correction. After the abnormal photovoltaic power output data points are corrected, the abnormal values ​​in the photovoltaic power output data will be replaced by the corrected values, resulting in a good photovoltaic power output dataset that can be used for the division of typical photovoltaic power output scenarios and prediction error modeling.

[0020] Furthermore, in step 2, based on typical photovoltaic power output scenarios, a probability distribution model for photovoltaic power output prediction errors is constructed. The specific method is as follows:

[0021] Step 2.1: Based on the adaptive K-means clustering algorithm, typical photovoltaic power output scenarios in the distribution network are identified, resulting in typical distributed photovoltaic power output curves.

[0022] The K-means algorithm uses Euclidean distance to evaluate the similarity between two samples. It randomly selects k points in the photovoltaic power output data as the initial cluster centers. The cluster centers are continuously updated by calculating the Euclidean distance from the photovoltaic power output value to the center at each time until the error function reaches and stabilizes at the minimum value.

[0023] Photovoltaic output value x in the sample i With x j The Euclidean distance between them is calculated using the formula (4):

[0024]

[0025] The magnitude of the square criterion error function is used to determine whether the cluster centers have reached stability. When the error function reaches and stabilizes at its minimum value, it indicates that the cluster centers of photovoltaic power output have stopped changing. The formula for calculating the square criterion error function is shown in equation (5):

[0026]

[0027] In the formula, k is the number of clusters; t i n is the number of samples in the i-th class; i It is the mean of the i-th class of samples;

[0028] The silhouette coefficient is used to measure the clustering effect of typical photovoltaic power output scenarios. Its calculation includes cohesion and separation. The formula for calculating the silhouette coefficient is as follows:

[0029]

[0030] In the formula, a(i) is the cluster cohesion, which is defined as the average distance between data points in the same category; b(i) is the inter-cluster separation, which is defined as the average distance between a sample point and data points in adjacent clusters. As can be seen from formula (6), the maximum value of the silhouette coefficient is 1 and the minimum value is 0. The closer the silhouette coefficient is to 1, the farther apart the two clusters are separated, the denser the distribution within the cluster, and the better the clustering effect.

[0031] Step 2.2: Based on meteorological conditions, BiLSTM is used to perform ultra-short-time forecasting of distributed photovoltaic power output to obtain the forecast curve of photovoltaic power output. The forecast value is compared with the actual value of typical power output scenarios to form a distribution map of forecast error.

[0032] BiLSTM consists of two layers of LSTM. Based on the BiLSTM neural network model, short-term prediction results of photovoltaic power output are obtained.

[0033] To evaluate the training results of the neural network, the root mean square error (RMSE) and mean square error (MAE) are used as evaluation metrics for the neural network's prediction of photovoltaic power output. The expressions for RMSE and MAE are as follows:

[0034]

[0035]

[0036] In the formula, N represents the total number of data points; f represents the predicted value of photovoltaic output; i This represents the actual value of photovoltaic power output;

[0037]

[0038] Divide the day into 15-minute intervals, resulting in 96 intervals in a day. Compare the predicted value at each interval with the actual value of the typical output scenario of the day to calculate and form a distribution map of the prediction error.

[0039] Step 2.3: Based on the distribution map of the prediction error, KDE is used to model the photovoltaic power output prediction error to obtain the probability distribution curve of the photovoltaic power output prediction error;

[0040] The expression for the kernel density estimate function is as follows:

[0041]

[0042] In the formula, N represents the total number of data points; h represents the bandwidth of the kernel density function, which is used to control the width of the kernel function and thus affect the smoothness of the density estimation; K is the kernel function, which is a probability density function with an integral of 1.

[0043] Furthermore, in step 3, the probabilistic power flow of the distribution network is calculated by combining the semi-invariants and Gram-Charlier series expansion method. The specific method is as follows:

[0044] Step 3.1: Use the deterministic power flow calculation method to give the power flow distribution under normal operation, thereby obtaining the state variable X at the reference operating point and calculating the sensitivity matrix S;

[0045] The nodal power equations of the power system are:

[0046]

[0047] In the formula, P i Q i V represents the injection of active and reactive power at node i, respectively; i θ i G represents the magnitude and angle of the voltage at node i, respectively; ij B ij These are the real and imaginary parts of the admittance matrix elements, respectively;

[0048] In stochastic power flow models, node injection includes active and reactive power injected by nodes, and state variables include node voltage magnitude and angle, expressed as:

[0049]

[0050] In the formula, S0 and X0 are the expected values ​​of the node injection amount S and the state variable X, respectively; ΔS and ΔX are random disturbances, which are regarded as random variables following a certain distribution.

[0051] Step 3.2: Based on the known probabilistic characteristics of the generator set and load, calculate the origin moment or central moment of the injected power at each node, and then determine its semi-invariants of each order.

[0052] For node load power, its random component is considered to be caused by the prediction error of photovoltaic output. This random component is described by a normally distributed random variable. When the load power changes according to a certain load curve, it is simulated by a discrete random distribution.

[0053] For injection power with a normal distribution, its first-order semi-invariant is equal to the expected value, the second-order semi-invariant is the variance of the normal distribution, and the third to sixth-order semi-invariants are zero. Semi-invariants are a numerical characteristic of random variables, which are obtained from the moments of random variables of orders no higher than the corresponding order.

[0054] The central moments of a random variable are expressed as follows:

[0055]

[0056] In the formula, μ represents the expected value; p v Represents the probability value;

[0057] semi-invariants K of each order i Distance from center M i The relationship is as follows:

[0058]

[0059] Step 3.3: Expand the probability density function F(x) and probability distribution function f(x) of the voltage distribution using Gram-Charlier series expansion, and express the coefficients of the series expansion in terms of semi-invariants. The expansion is shown below:

[0060]

[0061] In the formula: F(x) is the probability density function; f(x) is the probability distribution function; g v For each order of normalized semi-invariant, v = 1, 2, 3, 4, 5, 6; It is the standard normal distribution density function; It is a Hermite polynomial;

[0062] Step 3.4: Use the probability distribution of voltage at each node of the distribution network, including the node voltage probability density curve and the cumulative distribution curve, to describe the uncertainty of the power system in the form of a probability distribution.

[0063] Furthermore, in step 4, the probability of voltage exceeding the limit at the nodes of the distribution network is calculated, and the specific method for assessing the risk of voltage exceeding the limit in the distribution network is as follows:

[0064] The probability distribution of voltage at each node in the distribution network is obtained through probabilistic power flow calculation. A threshold value for the node voltage is set; when the voltage exceeds this value, the distribution network is considered to be at risk of exceeding the threshold. The probability of voltage exceeding the threshold is calculated based on the node voltage probability distribution, as shown in the following formula:

[0065]

[0066] In the formula, U i,t u represents the voltage at node i at time t; max u min R(U) represents the upper and lower limits of the system voltage constraint, respectively; i,t ) represents the probability that the system voltage exceeds the limit at time t.

[0067] A distribution network risk assessment system based on photovoltaic power output prediction error is provided. The system implements the aforementioned distribution network risk assessment method based on photovoltaic power output prediction error to achieve distribution network risk assessment based on photovoltaic power output prediction error.

[0068] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned distribution network risk assessment method based on photovoltaic power output prediction error, thereby achieving distribution network risk assessment based on photovoltaic power output prediction error.

[0069] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the control method of the multi-operating-state three-phase motor driver described above is implemented, and the distribution network risk assessment method based on photovoltaic power output prediction error is implemented, thereby realizing the distribution network risk assessment based on photovoltaic power output prediction error.

[0070] Compared with existing technologies, this invention has the following technical advantages: ① BiLSTM can provide relatively accurate prediction errors through accurate photovoltaic power output prediction. Combined with KDE, these errors can be modeled in detail with probability distribution, revealing the potential patterns and characteristics of the errors, which helps to more accurately assess the risks brought by photovoltaic power output prediction errors to the operation of the distribution network; ② By comprehensively considering constraints such as power supply constraints, current constraints, and distributed photovoltaic power output constraints, and combining semi-invariants and Gram-Charlier series expansion methods to calculate the probabilistic power flow of the distribution network, the probability density function and probability distribution function of the voltage distribution obtained from the probabilistic power flow calculation results are reduced, resulting in faster calculation speed and higher accuracy. Attached Figure Description

[0071] Figure 1 This is a flowchart of a distribution network risk assessment method based on photovoltaic power output prediction errors.

[0072] Figure 2 This is a typical output curve for distributed photovoltaic systems.

[0073] Figure 3 This is a residual distribution diagram of photovoltaic power output prediction.

[0074] Figure 4 This is a probability distribution diagram of the photovoltaic power output prediction error.

[0075] Figure 5 This is a cumulative probability curve of voltage at 33 nodes in the distribution network under small error conditions.

[0076] Figure 6 This is a cumulative probability curve of voltage at 33 nodes in the distribution network under large error conditions. Detailed Implementation

[0077] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0078] A method for risk assessment of distribution networks based on photovoltaic power output prediction errors includes the following steps:

[0079] Step 1: Merge and process the massive historical data of distributed photovoltaic power output to obtain power output data after correcting outliers.

[0080] Photovoltaic data was collected daily at 96 time points over two years. Many missing values ​​and zero values ​​were identified, collectively referred to as outliers. The Isolation Forest algorithm is suitable for extracting outliers from photovoltaic power output data caused by equipment problems or human error. The Isolation Forest algorithm considers sparse data points far from denser clusters as outliers, offering advantages such as high accuracy and low computational cost, making it ideal for massive data scenarios. Its main process is as follows:

[0081] Step 1.1: Construct an isolation tree to isolate abnormal photovoltaic output data points as early as possible by gradually segmenting the data points.

[0082] (1) Extract n sample data from the photovoltaic power output historical dataset with or without replacement, construct a data subset, and construct an initial binary tree iTree.

[0083] (2) Specify a feature dimension q=96 according to the daily time scale, and randomly select a cut point p in the current data that is between the maximum and minimum values ​​of the current node data feature q.

[0084] (3) At point p, divide the current photovoltaic output data space into two subspaces, left and right. Place attribute value data items with values ​​less than p into the left subspace, and attribute value data items with values ​​greater than p into the right subspace.

[0085] (4) Repeat steps (2) and (3) until the subspace can no longer be cut or the iTree has reached the initially defined limit height.

[0086] Step 1.2: Calculate the isolated path length of each output data point in the isolated forest and obtain the corresponding anomaly score to detect abnormal data points.

[0087] For the data to be tested, x is substituted into each iTree, and h(x) represents the height of the data falling on each iTree. E(h(x)) is the average of all h(x), and H(x) is the harmonic number. Because the structure of iTree is similar to that of binary search tree, the average path length l(n) of constructing a binary tree for n samples is:

[0088] l(n)=2H(n-1)-[2(n-1) / n](1)

[0089] H(i)=ln(i)+0.5772(2)

[0090] Define an anomaly score for a test data point as:

[0091]

[0092] The closer u(x,n) is to 1, the greater the probability that the data is outlier.

[0093] When u(x,n) is greater than 0.75, the data is considered an outlier and removed from the original photovoltaic power output dataset. The nearest neighbor interpolation method is used to correct the outlier data, and the corrected value is used to replace the original outlier, resulting in a good photovoltaic power output dataset that can be used for the division of typical photovoltaic power output scenarios and prediction error modeling.

[0094] Step 2: Based on typical photovoltaic power output scenarios, construct a probability distribution model for photovoltaic power output prediction errors.

[0095] Based on the corrected historical photovoltaic (PV) output data, an adaptive K-means clustering algorithm is used to cluster typical PV output scenarios. Taking into account various meteorological conditions, BiLSTM is used to perform ultra-short-term (UST) prediction of distributed PV output, resulting in UST prediction curves and an initial distribution map of prediction errors. Finally, probability distribution modeling is performed on the prediction errors. The specific process is as follows:

[0096] Step 2.1: Based on the adaptive K-means clustering algorithm, the typical output scenarios of photovoltaic power generation in the distribution network are divided, and the typical output curve of distributed photovoltaic power generation is obtained.

[0097] In the K-means algorithm, Euclidean distance is generally used to evaluate the similarity between two samples. It randomly selects k points in the photovoltaic power output data as the initial cluster centers. The day is divided into 15-minute intervals, so k = 96. The cluster centers are continuously updated by calculating the Euclidean distance from the photovoltaic power output value at each time to the center until the error function reaches and stabilizes at the minimum value.

[0098] Photovoltaic output value x in the sample i With x j The Euclidean distance between them is calculated using the formula (4):

[0099]

[0100] The magnitude of the square criterion error function is used to determine whether the cluster centers have reached stability. When the error function reaches and stabilizes at its minimum value, it indicates that the cluster centers have stopped changing. The formula for calculating the square criterion error function is shown in equation (5):

[0101]

[0102] In the formula, k is the number of clusters; t i n is the number of samples in the i-th class; i It is the mean of the i-th class of samples;

[0103] The profile coefficient can be used to measure the clustering effect of typical photovoltaic power output scenarios. Its calculation includes cohesion and separation. The formula for calculating the profile coefficient is:

[0104]

[0105] In the formula, a(i) is the intra-cluster cohesion, defined as the average distance between data points in the same cluster; b(i) is the inter-cluster separation, defined as the average distance between a sample point and data points in adjacent clusters. As can be seen from formula (6), the maximum value of the silhouette coefficient is 1 and the minimum value is 0. The closer the silhouette coefficient is to 1, the farther apart the two clusters are, the denser the intra-cluster distribution, and the better the clustering effect.

[0106] Step 2.2: Based on meteorological conditions such as solar radiation, temperature, and humidity, BiLSTM is used to perform ultra-short-time prediction of distributed photovoltaic power output, and the prediction curve of photovoltaic power output is obtained. The predicted value is compared with the actual value of typical power output scenarios to form a distribution map of prediction error.

[0107] BiLSTM consists of two layers of LSTM. Based on the BiLSTM neural network model, short-term predictions of photovoltaic power output are obtained. To evaluate the training results of the neural network, the root mean square error (RMSE) and mean square error (MAE) are used as evaluation metrics for the neural network's photovoltaic power output prediction. The expressions for RMSE and MAE are as follows:

[0108]

[0109] In the formula, N represents the total number of data points; f represents the predicted value of photovoltaic output; i This represents the actual value of photovoltaic power output;

[0110]

[0111] Divide the day into 15-minute intervals, resulting in 96 intervals in a day. Calculate the residual between the predicted value at each interval and the actual value of the typical output scenario for that day to form a distribution map of the prediction error.

[0112] Step 2.3: Based on the distribution map of the prediction error, KDE is used to model the photovoltaic power output prediction error, and the probability distribution curve of the photovoltaic power output prediction error is obtained. The expression of the kernel density estimation function is as follows:

[0113]

[0114] In the formula, N represents the total number of data points; h represents the bandwidth of the kernel density function, which controls the width of the kernel function and thus affects the smoothness of the density estimation; K is the kernel function, which is a probability density function with an integral of 1.

[0115] In summary, BiLSTM can provide relatively accurate prediction errors through accurate photovoltaic power output prediction. When combined with KDE, these errors can be modeled in detail with probability distribution. The model is a prediction error probability distribution curve that approximates a normal distribution.

[0116] Step 3: Calculate the probabilistic power flow of the distribution network using a combination of semi-invariants and Gram-Charlier series expansions.

[0117] Step 3.1: Use deterministic power flow calculation methods to obtain the power flow distribution under normal operating conditions, thereby obtaining the state variable X at the reference operating point, and then calculate the sensitivity matrix S.

[0118] The probabilistic power flow calculation method uses a linearized model based on the Newton-Raphson power flow calculation.

[0119] The nodal power equations of the power system are:

[0120]

[0121] In the formula, P i Q i V represents the injection of active and reactive power at node i, respectively; i θ i G represents the magnitude and angle of the voltage at node i, respectively; ij B ij These are the real and imaginary parts of the admittance matrix elements, respectively.

[0122] In stochastic power flow models, node injection includes active and reactive power injected by nodes, and state variables include node voltage magnitude and angle, which can be expressed as:

[0123]

[0124] In the formula, S0 and X0 are the expected values ​​of the node injection amount S and the state variable X, respectively; ΔS and ΔX are random disturbances, which can be regarded as random variables following a certain distribution.

[0125] Step 3.2: Based on the known probabilistic characteristics of the generator set and load, calculate the origin moment or central moment of the injected power at each node, and then determine its semi-invariants of each order:

[0126] For node load power, its random component can be considered as being caused by prediction errors in photovoltaic output. This random component can generally be described by a normally distributed random variable. When the load power varies according to a certain load curve, it can be simulated using a discrete random distribution.

[0127] For injection power with a normal distribution, its first-order semi-invariant equals the expected value, the second-order semi-invariant is the variance of the normal distribution, and the third to sixth-order semi-invariants are zero. Semi-invariants are a numerical characteristic of a random variable, which can be obtained from the moments of random variables of orders no higher than the corresponding order.

[0128] The central moments of a random variable are expressed as follows:

[0129]

[0130] In the formula, μ represents the expected value; p v Represents the probability value;

[0131] According to equation (7), the semi-invariants K of each order can be obtained. i Distance from center M i The relationship is as follows:

[0132]

[0133] Step 3.3: Expand the probability density function F(x) and probability distribution function f(x) of the voltage distribution using Gram-Charlier series expansion, and express the coefficients of the series expansion in terms of semi-invariants. The expansion is shown below:

[0134]

[0135]

[0136] In the formula: F(x) is the probability density function; f(x) is the probability distribution function; g v For each order of normalized semi-invariant, v = 1, 2, 3, 4, 5, 6; It is the standard normal distribution density function; It is a Hermite polynomial;

[0137] Step 3.4: Consider various constraints and calculate the probabilistic power flow of the distribution network.

[0138] In the probabilistic power flow calculation, the following constraints are considered:

[0139] (1) Power supply constraints:

[0140] To suppress large power fluctuations in the distribution network, the power of the i-th power source needs to be constrained:

[0141]

[0142] In the formula, It is the power injected into the system by the power source at time t; and These are the upper and lower power limits of the power injection system, respectively.

[0143] (2) Distribution network branch current constraints:

[0144] I ij ≤I ij.max (18) In the formula, I ij.max It is the upper limit of the branch current amplitude between node i and node j.

[0145] (3) Operational constraints of distributed photovoltaic power generation:

[0146]

[0147] In the formula, These are the active power and reactive power of the distributed photovoltaic power source, respectively. This represents the maximum output of a distributed photovoltaic (PV) power source; the power factor of a distributed PV power source. The value is 0.95.

[0148] Considering the randomness of photovoltaic power output prediction errors under different typical power output scenarios, the probability distribution of voltage at each node of the distribution network is obtained by combining semi-invariants and Gram-Charlier expansion series, including point voltage probability density curves and cumulative distribution curves. That is, the probability distribution of distribution network node voltage is used as the calculation result of probability power flow, and the uncertainty of the system is described in the form of voltage probability distribution, and the operating status of the system is analyzed accordingly.

[0149] Step 4: Calculate the probability of voltage exceeding the limit at the nodes of the distribution network and assess the risk of voltage exceeding the limit in the distribution network.

[0150] The probability distribution of voltage at each node in the distribution network is obtained through probabilistic power flow calculation. A limit value for the node voltage is set; when the voltage exceeds this value, it is considered that the distribution network has exceeded its limits. The probability of voltage exceeding the limit is calculated based on the node voltage probability distribution, as shown in the following formula:

[0151]

[0152] In the formula, U i,t u represents the voltage at node i at time t; max u min R(U) represents the upper and lower limits of the system voltage constraint, respectively; i,t ) represents the probability that the system voltage exceeds the limit at time t.

[0153] An adaptive K-means algorithm is used to cluster historical data of distributed photovoltaic power output. Typical distributed photovoltaic power output scenarios are as follows: Figure 2 As shown. According to the silhouette coefficient curve, when the number of clusters k=4, the silhouette coefficient is closest to 1, indicating that the clustering effect of the four scenarios is the best. The typical distributed output curves obtained by the division are compared with the actual photovoltaic output curves of the distribution network, and the four typical processed curves are named sunny day scenario, cloudy day scenario, cloudy and rainy day scenario, and rainy and snowy day scenario, respectively.

[0154] This invention uses a 33-node radial distribution network of IEEE as a simulation example, with distributed photovoltaic (PV) power sources connected to 12 nodes and a power factor set to 0.95. A sunny day scenario is selected as a typical scenario for the distributed PV output on the following day. The residual distribution for PV output prediction using a BiLSTM neural network is shown below. Figure 3 As shown.

[0155] Based on KDE, a probability density distribution model of photovoltaic power output error is performed, and the probability distribution of the prediction error is as follows: Figure 3 As shown, by Figure 4 As can be seen, the KDE method can include most observation points, has high fitting accuracy, and can present the probability distribution of prediction error results well.

[0156] Based on the aforementioned distributed photovoltaic power prediction error curve, the probabilistic power flow of the distribution network is calculated using the semi-invariant and Gram-Charlier expansion series method, and compared with the results of the probabilistic power flow calculated by the Monte Carlo (MTCR) method, where the number of iterations of the MTCR method is set to 5000.

[0157] During the operation of a distribution network, weather fluctuations may cause discrepancies between forecast information and the current state. In such cases, the forecast error of photovoltaic (PV) processing becomes an uncertainty factor in the operation of the distribution network. If the forecast error is too large, the difference between the predicted and actual PV output will cause a significant disturbance to the operation of the distribution network, leading to voltage fluctuations at the distribution network nodes. Table 1 shows the voltage over-limit probability and simulation calculation time of node 33 of the distribution network under large and small errors. The cumulative probability distribution of the voltage at node 33 is shown in Table 1. Figure 5 , Figure 6 As shown.

[0158] Table 1. Comparison of voltage over-limit probability and simulation time under large and small errors.

[0159]

[0160] Table 2 shows that the magnitude of the photovoltaic output prediction error directly affects the voltage over-limit probability of the distribution network. With small errors, the voltage over-limit probability is only around 0.01, but as the error increases, the probability increases nearly threefold, approaching 0.3. Although the calculation accuracy of the probabilistic power flow using semi-invariant methods and Gram-Charlier expansions is slightly lower than that of the Monte Carlo method, the simulation time is significantly reduced. Therefore, using semi-invariant methods and Gram-Charlier expansions for probabilistic power flow calculations saves considerable computation time with only a slight decrease in accuracy, making it more suitable for short-term and ultra-short-term real-time risk assessment scenarios in distribution networks.

[0161] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A power distribution network risk assessment method based on photovoltaic power output prediction error, characterized in that, The method comprises the following steps: Step 1, constructing an isolated tree of an isolated forest algorithm, and performing fusion processing on massive distributed photovoltaic output historical data to correct abnormal values of photovoltaic output; Step 2, constructing a probability distribution model of photovoltaic output prediction error based on a typical photovoltaic output scene, wherein the typical photovoltaic output scene of the power distribution network is divided based on an adaptive K-means clustering algorithm, the distributed photovoltaic output is super-short-time predicted based on BiLSTM according to meteorological conditions, a photovoltaic output prediction curve is obtained, and the photovoltaic output prediction error is modeled by using KDE to obtain a probability distribution curve of the photovoltaic output prediction error; Step 3, combining the method of semi-invariant and Gram-Charlier expansion series, the probability distribution of the node voltage of the power distribution network is obtained through probability power flow calculation, including a node voltage probability density curve and a probability distribution curve, and the uncertainty of the system is described in the form of probability distribution; Step 4, calculating the node voltage out-of-limit probability of the power distribution network to evaluate the voltage out-of-limit risk of the power distribution network.

2. The method for risk assessment of power distribution network based on photovoltaic power output prediction error according to claim 1, wherein, In step 1, the massive distributed photovoltaic output historical data is fused and processed to correct abnormal values of photovoltaic output, and the specific method is as follows: Step 1.1, constructing an isolated tree of an isolated forest algorithm, and isolating photovoltaic output abnormal data points by gradually dividing data points; First, randomly select n sample data points from massive photovoltaic output data as a subsample set, construct an initial iTree, and put the subsample set into the root node of the tree; then randomly specify an attribute dimension q from multiple dimensions of the data, and randomly generate a cutting point p in the current node data; then generate a hyperplane at the cutting point, divide the data space of the current node into two subspaces, and put the data items with the specified q attribute value less than p into the left subspace of the current node; otherwise, put them into the right subspace; recursively call the above steps until the subspace cannot be further cut or the iTree has reached the limited height; Step 1.2, calculating the isolated path length of each output data point in the isolated forest, and obtaining the corresponding abnormal score to detect abnormal data points; For test data x, substitute it into each iTree in the forest, calculate its depth h(x) in each tree, calculate the average value of all h(x) as E(h(x)), and calculate the abnormal score of the test data combined with the standard average search length l(n) and the harmonic number H(x); The standard average search length l(n) and the harmonic number H(x) are set as follows: l(n)=2H(n-1)-[2(n-1) / n] (1) H(i)=ln(i)+0.5772 (2) Then the abnormal score of the test data is: If u(x,n) is close to 1, the data is considered to be abnormal data; for abnormal data, the nearest neighbor interpolation method is used for correction, and after the abnormal photovoltaic output data points are corrected, the abnormal values in the photovoltaic output data are replaced by the corrected values, and a good photovoltaic output data set for photovoltaic output typical scene division and prediction error modeling is obtained.

3. The method for risk assessment of power distribution network based on photovoltaic power output prediction error according to claim 1, characterized in that, In step 2, based on typical photovoltaic output scenarios, a probability distribution model of photovoltaic output prediction error is constructed, and the specific method is as follows: In step 2.1, the typical photovoltaic output scenarios of the distribution network are divided based on the adaptive K-means clustering algorithm, and the typical photovoltaic output curve is obtained, The K-means algorithm uses the Euclidean distance to evaluate the similarity of two samples, randomly selects k points in the photovoltaic output data as the initial clustering center, and constantly updates the clustering center by calculating the Euclidean distance of the photovoltaic output value at each time to the center until the error function reaches and stabilizes at the minimum value. The photovoltaic output value x in the sample i The Euclidean distance between x j The calculation formula is shown as formula (4): The size of the squared criterion error function is used to determine whether the clustering center has reached stability. When the error function reaches and stabilizes at the minimum value, it means that the clustering center of the photovoltaic output has not changed. The calculation formula of the squared criterion error function is shown in equation (5): In the formula, k is the number of clusters. t i n is the number of samples in class i; n i is the mean of the samples in class i; The size of the silhouette coefficient is used to measure whether the clustering effect of the typical photovoltaic output scenario is good. The calculation includes cohesion and separation. The silhouette coefficient calculation formula is: In the formula, a(i) is the cohesion within the cluster, defined as the average distance between data points in the same class; b(i) is the separation between clusters, defined as the average distance between sample points and data points in adjacent clusters. As can be seen from equation (6), the maximum value of the silhouette coefficient is 1 and the minimum value is 0. The closer the silhouette coefficient is to 1, the farther the two clusters are separated, the more densely distributed the clusters are, and the better the clustering effect is. In step 2.2, according to the weather conditions, the BiLSTM is used to perform ultra-short-term prediction of the distributed photovoltaic output, and the prediction curve of the photovoltaic output is obtained. The prediction error distribution graph is formed by comparing the predicted value with the actual value of the typical output scenario. BiLSTM is composed of double-layer LSTM. According to the BiLSTM neural network model, the short-term prediction result of the photovoltaic output is obtained. To evaluate the training result of the neural network, the root mean square error RMSE and the mean square error MAE are used as the evaluation indicators of the neural network for photovoltaic output prediction. The expressions of RMSE and MAE are as follows: In the formula, N represents the total number of data points; represents the predicted value of photovoltaic output; f i represents the actual value of photovoltaic output; Divide a day into 96 time points according to every 15 minutes. Compare the predicted value of each time point with the actual value of the typical output scenario of the day to form the prediction error distribution graph. In step 2.3, based on the prediction error distribution graph, the KDE is used to model the photovoltaic output prediction error, and the probability distribution curve of the photovoltaic output prediction error is obtained. The expression of the kernel density estimation function is as follows: In the formula, N represents the total number of data points; h represents the bandwidth of the kernel density function, which is used to control the width of the kernel function and thus affects the smoothness of the density estimation; K is the kernel function, which is a probability density function with an integral of 1.

4. The method for risk assessment of power distribution network based on photovoltaic power output prediction error of claim 1, wherein, In step 3, the probability power flow of the distribution network is calculated by combining the semi-invariant and Gram-Charlier expansion series method, and the specific method is as follows: In step 3.1, the deterministic power flow calculation method is used to give the power flow distribution under normal operation, so as to obtain the state variable X at the reference operating point and the sensitivity matrix S. The node power equation of the power system is as follows: where P i , Q i are the active and reactive power injections at node i; V i , θ i are the magnitude and angle of the voltage at node i; G ij , B ij are the real and imaginary parts of the admittance matrix elements; In the stochastic power flow model, the nodal injection includes the active power and the reactive power injected by the nodes, and the state variable includes the voltage amplitude and the angle of the nodes, which is expressed as: In the formula, S0 and X0 are the expected values of the nodal injection S and the state variable X respectively; and ΔS and ΔX are random disturbances, which are regarded as random variables obeying a certain distribution; Step 3.2: According to the known probabilistic description characteristics of the generator set and the load, the origin moment or the central moment of the injection power of each node is calculated, and then the semi-invariants of each order are obtained; For the nodal load power, the random component is regarded as being caused by the prediction error of the photovoltaic output, and the random component is described by a normal distribution random variable. When the load power varies according to a certain load curve, a discrete random distribution is used for simulation; For the normal distribution injection power, the first-order semi-invariant is equal to the expected value, the second-order semi-invariant is the variance of the normal distribution, and the third-order to sixth-order semi-invariants are zero. The semi-invariant is a numerical characteristic of the random variable, which is obtained from the moments of the random variable of not higher than the corresponding order; The central distance of the random variable of each order is expressed as: In the formula, μ represents an expected value; p v represents a probability value; The semi-invariants K of each order i The relationship between the center distance M i is shown as follows: Step 3.3: The probability density function F(x) and the probability distribution function f(x) of the voltage distribution are expanded by using the Gram-Charlier series, the semi-invariants are used to express the coefficients of the series expansion, and the expansion is as follows: where: F(x) is the probability density function; f(x) is the probability distribution function; g v are the normalized semi-invariants of order v = 1, 2, 3, 4, 5, 6; is the standard normal distribution density function; is the Hermite polynomial; Step 3.4: The probability distribution of each node voltage of the distribution network, including the node voltage probability density curve and the cumulative distribution curve, is used to describe the uncertainty of the power system in the form of probability distribution.

5. The method for risk assessment of power distribution network based on photovoltaic power output prediction error of claim 1, wherein, In step 4, the node voltage out-of-limit probability of the distribution network is calculated, and the specific method for evaluating the voltage out-of-limit risk of the distribution network is as follows: The probability distribution of each node voltage of the distribution network is obtained by the probabilistic power flow calculation, the out-of-limit value of the node voltage is set, the voltage out-of-limit risk of the distribution network can be considered when the voltage exceeds the value, the voltage out-of-limit probability is calculated according to the node voltage probability distribution, and the calculation formula is as follows: In the formula, U i,t represents the voltage of node i at time t; u max , u min respectively represent the upper limit and lower limit of the system voltage constraint; R(U i,t ) represents the probability of system voltage out-of-limit at time t.

6. A power distribution grid risk assessment system based on photovoltaic output prediction errors, characterized by, The photovoltaic output prediction error-based risk assessment method for the distribution network according to any one of claims 1-5 is implemented, and the photovoltaic output prediction error-based risk assessment for the distribution network is realized.

7. A computer device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the computer program, the photovoltaic output prediction error-based risk assessment method for the distribution network according to any one of claims 1-5 is implemented, and the photovoltaic output prediction error-based risk assessment for the distribution network is realized.

8. A computer readable storage medium, having a computer program stored thereon, wherein when the computer program is executed by a processor, the photovoltaic output prediction error-based risk assessment method for the distribution network according to any one of claims 1-5 is implemented, and the photovoltaic output prediction error-based risk assessment for the distribution network is realized.

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