Risk Assessment of Distribution Network Operation Based on Generalized Load

Abstract

With the widespread use of distributed generation and electric vehicles, the uncertainty of distribution network operation is increased, challenging risk assessment. This paper proposes a generalized load modeling and risk assessment method based on GNG–Informer–WOA. GNG adaptively clusters load curves to identify typical patterns and noise; WOA optimizes Informer’s hyperparameters for high-precision prediction. An index system covering voltage out-of-limit, regulation capacity, and new energy consumption risks is established, with weights determined by fusing AHP and PCA via game theory. Case studies on the improved IEEE 33-bus system show the method effectively characterizes generalized load characteristics and accurately evaluates risks under different scenarios, supporting safe operation.

1. Introduction

With the advancement of the dual-carbon strategic goal and the accelerated construction of new-type power systems, the distribution network has evolved from a traditional passive power distribution link into a core hub for grid connection and consumption of distributed generation (DG), electric vehicles (EV), energy storage and other generalized load resources. Accurate and quantitative operation risk assessment is the core basis to ensuring the safe, stable and economic operation of the distribution network, and also a key technical support for grid operation scheduling, risk early warning and active control.

However, high-proportion and large-scale accessing of generalized loads has brought strong randomness, non-linearity and long-sequence time-series volatility to distribution network operation. The traditional operation mode of the distribution network has undergone fundamental changes: problems such as frequent node voltage out-of-limit, bidirectional power flow fluctuation, insufficient flexible regulation capacity, and new energy consumption difficulties have become increasingly prominent. The operation risk of the distribution network presents the characteristics of multi-source coupling, multi-scenario differentiation and strong uncertainty, which brings severe challenges to the traditional risk assessment theory and method system. It is urgent to carry out in-depth research on generalized load modeling and operation risk assessment methods for new-type distribution networks, to effectively identify and quantify potential operation risks, and provide scientific decision-making basis for the safe operation of the distribution network.

A reasonable risk assessment index system is the foundation for quantification, but no unified standard exists. Scholars have proposed indicators considering high-permeability wind power [1], wind energy correlation [2], voltage/power flow out-of-limit [3], weather conditions [4], and EV access [5,6]. Comprehensive index systems covering risk severity, probability [7,8], and weight have also been constructed [9]. However, the existing risk assessment index systems mostly focus on single risks such as voltage or power flow out-of-limit under the traditional operation mode, and lack a systematic and comprehensive index system covering voltage safety, flexible regulation capacity and new energy consumption capacity of a distribution network under high-proportion generalized load access. It is difficult to fully characterize the multi-dimensional and multi-source coupling operation risks of new-type distribution networks, leading to one-sided risk assessment results.

In terms of assessment methods, they are mainly divided into weighted and non-weighted categories. Weighted methods (AHP [10], Delphi [11], entropy weight method [12]) are simple to calculate but subjective. Derivative methods include the dynamic inertia algorithm [13] and improved entropy weight method [14,15]. Non-weighted methods (PCA [16,17,18], data envelopment analysis [19], fuzzy comprehensive evaluation [20]) avoid subjective weighting [21,22], but are complex and often only achieve qualitative evaluation, limiting practical application [23]. On the whole, the existing subjective weighting methods are highly dependent on expert experience, with strong subjectivity and poor adaptability to complex and changeable operation scenarios, while objective weighting methods are easily affected by data outliers and noise, and cannot effectively integrate the engineering experience of actual distribution network operation. Most existing studies fail to realize the effective fusion of subjective and objective weighting methods, and it is difficult to balance the rationality and accuracy of index weight calculation, which restricts the accuracy and engineering application value of the final risk assessment results.

To address the above key technical bottlenecks and research gaps, this paper proposes a complete set of distribution network operation risk assessment methods based on high-precision generalized load modeling. The main research contents and core innovations are as follows:

(1)

A non-mechanistic generalized load modeling method based on GNG-Informer-WOA fusion is proposed. The growing neural gas (GNG) algorithm realizes adaptive clustering of generalized load curves and noise data identification, solving the defect that traditional clustering algorithms need to pre-set the number of clusters and are sensitive to abnormal data; the whale optimization algorithm (WOA) optimizes the key hyperparameters of the Informer model, realizing high-precision prediction of generalized load time-series characteristics, and providing high-confidence input data for subsequent risk assessment.

(2)

A game theory-based combined weighting method is proposed, which integrates analytic hierarchy process (AHP) and principal component analysis (PCA) to calculate index weights, effectively balancing the subjective experience of experts and the objective characteristics of operation data, and realizing accurate quantitative assessment of the comprehensive operation risk of the distribution network.

Finally, the effectiveness and superiority of the proposed method are verified based on the improved IEEE 33-bus system. The research results can provide a scientific decision-making basis for the safe and stable operation of the new-type distribution network with high-proportion generalized load access, and have important theoretical significance and engineering application value.

2. Generalized Load Modeling of Distribution Networks Based on GNG-Informer-WOA Synthesis Algorithm

The accuracy of distribution network operation risk assessment is highly dependent on the precise characterization of generalized load characteristics. However, the strong randomness, multi-scenario fluctuation and non-linear characteristics of generalized loads bring core challenges to traditional mechanism-based load modeling methods, which are prone to problems such as insufficient modeling accuracy and weak generalization ability. To solve this problem, this section proposes a generalized load, non-mechanistic modeling method based on GNG-Informer-WOA fusion, which realizes accurate characterization of generalized load characteristics from three dimensions (load pattern clustering, time-series prediction and adaptive hyperparameter optimization), and provides high-confidence input data for subsequent risk assessment. This section will sequentially introduce the overall framework of the modeling method, the principle and implementation process of the core sub-models, and the specific execution steps of modeling.

2.1. Overview of GNG-Informer-WOA Modeling

The generalized load modeling process integrates three core technologies: GNG for load clustering, Informer for sequence prediction, and WOA for hyperparameter optimization, aiming to achieve accurate identification of typical load patterns and high-precision prediction of load characteristics.

The specific structure of the improved load clustering method is shown in Figure 1.

Figure 1 shows the complete implementation framework of the GNG clustering algorithm. The algorithm first normalizes and standardizes the original generalized load data, then realizes the adaptive clustering of load curves through the competitive learning module, Hebbian weight update module and growth/pruning mechanism. It finally identifies the isolated noise data through the noise identification module, and outputs the typical load patterns. Compared with the traditional K-means and DBSCAN clustering algorithms, the GNG algorithm can adaptively determine the optimal number of clusters without pre-setting the cluster number, and can effectively eliminate the interference of abnormal load curves on the subsequent prediction modeling. The high-quality typical load patterns obtained by clustering lay a solid foundation for the construction of the sub-prediction model for each load type in the subsequent steps.

Compared with traditional clustering algorithms (K-means, DBSCAN) widely used in load modeling, the GNG algorithm adopted in this paper has significant advantages: (1) K-means needs to pre-set the number of clusters, which makes it difficult to adapt to the unknown load characteristics of generalized loads, while GNG can adaptively determine the optimal number of clusters through growth and pruning mechanisms. (2) DBSCAN is sensitive to the density threshold and easily misclassifies load curves with a small sample size, while GNG can effectively identify isolated noise data through competitive learning, with stronger robustness to abnormal load data. (3) GNG can maintain the topological structure of load data, and the clustering results have better intra-class compactness and inter-class separability, laying a better foundation for subsequent sub-model prediction.

Table 1. Core hyperparameters of the GNG clustering algorithm.

Hyperparameter	Value	Description
Maximum number of neurons	100	Upper limit of neurons in the GNG network to avoid over-expansion
Learning rate of winning neuron	0.05	Weight update coefficient of the neuron closest to the input sample
Learning rate of neighboring neurons	0.005	Weight update coefficient of the neighbor neurons of the winning neuron
Error decay coefficient	0.995	Decay factor of the accumulated error of neurons in each iteration
Maximum number of iterations	2000	Termination condition of algorithm iteration

presents the hyperparameter indicators for GNG clustering

To quantitatively verify the effectiveness of GNG clustering, we adopt three widely used clustering performance metrics:

• Silhouette Coefficient (SC): The intra-class compactness and inter-class separability of clustering results, with a value range of [−1, 1]. The closer to 1, the better the clustering effect.
• Calinski–Harabasz (CH) Index: The ratio of inter-class dispersion to intra-class dispersion. The larger the value, the better the clustering effect.
• Davies–Bouldin (DB) Index: The average similarity between each cluster and its most similar cluster. The smaller the value, the better the clustering effect.

The quantitative results of GNG clustering on the generalized load dataset are shown as follows: SC = 0.826, CH = 287.3, and DB = 0.312. The results show that the GNG algorithm can effectively identify typical load patterns, with excellent intra-class compactness and inter-class separability, and can effectively eliminate noise data interference.

To justify the choice of the GNG algorithm, we compared it with two widely used alternative clustering methods (K-means, DBSCAN) using the same dataset, and the results are shown in

Table 2. Clustering performance comparison of different algorithms.

Algorithm	Silhouette Coefficient	CH Index	DB Index
GNG (Proposed)	0.826	287.3	0.312
K-means	0.618	195.6	0.587
DBSCAN	0.703	221.4	0.456

.

The comparison results show that the proposed GNG algorithm has better clustering performance than K-means and DBSCAN. More importantly, GNG can adaptively determine the optimal number of clusters without manual pre-setting, and has stronger robustness to noise and abnormal load data, making it more suitable for generalized load modeling with strong uncertainty and multi-scenario characteristics.

2.2. Informer-WOA Model

By introducing the probsparse self-attention mechanism and self-attention distillation technology, Informer significantly reduces the computational complexity and memory consumption of traditional transformers, enabling it to efficiently capture the key dependencies in long sequences. The Informer model is composed of an encoder and a generative decoder. The encoder extracts sequence features through a multi-layer stacked probsparse self-attention layer and distillation operation. The decoder can predict the entire output sequence through a forward propagation, which greatly improves the efficiency of long sequence prediction.

Although the Informer neural network is powerful, the configuration of its super parameters (such as layers, attention heads, learning rate, etc.) has a significant impact on the performance of the model; it is difficult to manually adjust the parameters and easy to fall into local optimization. Therefore, this paper introduces the whale optimization algorithm (WOA). The whale optimization algorithm simulates the foraging behavior of humpback whales, and has stronger global exploration ability and fewer control parameters. It can be used to optimize the super parameters of a neural network and solve the problem of model configuration.

The whale optimization algorithm is mainly inspired by the hunting behavior of humpback whales. The basic idea is to simulate the process of surrounding prey, bubble net attack and random search of prey to find the optimal solution. In the WOA algorithm, the position of each individual whale represents a set of super-parametric combinations of the Informer model. The algorithm evaluates the advantages and disadvantages of the super-parameter combination by calculating the individual fitness value (such as the predicted mean square error), and iteratively updates the positions of all individuals by simulating the three behaviors of surrounding prey (approaching the current optimal solution), bubble net attack (spiral position update) and searching for prey (random exploration), and finally finds the super parameter configuration that makes the Informer model perform best. The network architecture of the proposed Informer-WOA model is shown in Figure 2.

For the load prediction link, we compare the proposed Informer-WOA model with mainstream alternatives, and the advantages are as follows: (1) Compared with traditional time-series prediction models (ARIMA, LSTM, GRU), the Informer model has a stronger ability to capture long-term dependencies of load sequences, and solves the problem of gradient disappearance and prediction accuracy degradation of RNN-based models in long-sequence prediction. (2) Compared with the manually tuned Informer model, the WOA-optimized Informer can automatically search the optimal hyperparameter combination (number of encoder/decoder layers, attention heads, learning rate, etc.), avoiding local optima caused by manual tuning. (3) Compared with other meta-heuristic optimization algorithms (particle swarm optimization, genetic algorithm), optimized Informer-WOA has stronger global exploration ability and fewer control parameters, with faster convergence speed and better optimization effect.

2.3. Model Description

At present, the general form of input and output of load modeling based on neural network can be described as follows:

$$\left\{\begin{array}{ll}\widehat{P}(t)=f_p[& P(t-1),\dots ,P(t-N_P);\\ & U(t-1),\dots ,U(t-N_P)]\\ \widehat{Q}(t)=f_q[& Q(t-1),\dots ,Q(t-N_Q);\\ & U(t-1),\dots ,U(t-N_Q)]\end{array}\right.$$

(1)

$\widehat{P}(t)$ and $\widehat{Q}(t)$ (MVar) are the final active and reactive power, respectively; $f_p$ and $f_q$ are the description functions of load active and reactive power; $P(t)$ and $Q(t)$ are the active power and reactive power at time; $U(t)$ is the voltage at time t; $N_P$ and $N_{\mathrm{q}}$ are the orders of active and reactive power, respectively, where $N_P$ = $N_Q$ = N.

Firstly, this paper uses GNG to cluster the original load data to identify the typical load patterns and eliminate the noise. Then, for each type of load mode, the Informer neural network optimized by WOA is used to accurately model the sample data through training. The specific steps are as follows:

(1)

Analyze the characteristics and influencing factors of the power load, and determine the main influencing factors of power load.

(2)

GNG is used to cluster the load curve. The number of clusters is automatically determined according to the density accessibility, the separated noise data is identified, and the parameters are repeatedly adjusted to obtain stable clustering results.

(3)

An Informer forecasting model is initialized for each load pattern clustering obtained in step 2.

(4)

The WOA optimization algorithm is used to optimize the hyperparameters of each Informer model (such as the number of encoder/decoder layers, attention headers, learning rate, etc.). Using the training data under this cluster, the fitness value (prediction mean square error) of individuals is calculated to obtain the optimal combination of super parameters.

(5)

The optimal hyperparameter configuration obtained by WOA optimization is assigned to the corresponding Informer model, and the final training of the model is completed on the training data of the cluster.

(6)

All trained Informer sub-models are tested on the validation set, and the overall prediction results are compared with the actual values to verify the effectiveness and accuracy of the model constructed in this section.

To evaluate the suitability of the proposed GNG-Informer-WOA pipeline for real-time grid monitoring and decision-making, we analyze its computational complexity, actual simulation efficiency and scalability as follows:

• Computational complexity analysis

GNG clustering module: The time complexity of the GNG algorithm is $O(N_{sample}·N_{neuron})$, where $N_{sample}$ is the number of load samples, and $N_{neuron}$ is the number of neurons in the GNG network. For 24 h of 15 min interval load data (96 sampling points per day), GNG clustering can be completed within 10 s. Notably, clustering only needs to be updated when load characteristics change significantly (e.g., seasonal changes), without real-time repeated calculation.

Informer-WOA prediction module: The time complexity of the Informer model is $O(L_{input}·\log L_{input})$, where $L_{input}$ is the length of the input sequence, which is significantly lower than the $O(L_{input}^2)$ complexity of the traditional transformer model. WOA hyperparameter optimization is completed offline in the model training stage; for online application, the trained model only needs forward propagation for prediction, with a single-step prediction time of less than 0.5 s for the IEEE 33-bus system.

Risk assessment module: The time complexity of index calculation and game theory weighting is $O(N_{node}·N_{sample})$, and the full-process risk assessment for 500 samples can be completed within 5 s for the IEEE 33-bus system.

2.

Actual simulation efficiency test

All simulations are carried out on a computer with an Intel Core i7-12700H CPU, 16 GB RAM, and NVIDIA RTX 3060 GPU. The offline training of the GNG-Informer-WOA model takes about 25 min for the 33-node system; for online application, after load data collection, the full process from load prediction to risk quantification can be completed within 8 s, which fully meets the 15 min level real-time monitoring and auxiliary decision-making requirements of medium-voltage distribution networks.

3.

Scalability analysis

The proposed pipeline has good scalability for large-scale distribution networks: (1) GNG clustering can be carried out by region, avoiding the exponential growth of calculation amount with the increase in node number. (2) The Informer model has natural advantages in long-sequence prediction, and can maintain high prediction efficiency when the number of nodes and sequence length increase. (3) Risk index calculation can be parallelized for each node and line, which can further improve calculation efficiency for large-scale systems. For distribution networks with more than 100 nodes, the online assessment time can still be controlled within 30 s through parallel computing, which is suitable for real-time monitoring and decision-making of actual distribution networks.

The combination of GNG-Informer-WOA realizes full-chain optimization of “clustering–prediction–modeling”; GNG clustering reduces the complexity of load modeling by classifying typical load patterns, the WOA-optimized Informer ensures high-precision prediction of each load pattern, and the combination of the three modules solves the core defects of traditional load modeling methods: low accuracy for generalized loads with strong volatility, poor adaptability to multi-scenario load characteristics, and the tendency to fall into local optima.

2.4. Generalized Load Forecasting Model Validation

To verify the effectiveness and superiority of the proposed GNG-Informer-WOA generalized load forecasting model, we carry out a quantitative performance evaluation, baseline method comparison and visual verification in this section.

Evaluation Metrics

To demonstrate the superiority of the proposed model, we selected three widely used baseline methods for comparison: (1) ARIMA (classical statistical time-series prediction model); (2) LSTM (mainstream recurrent neural network for load prediction); and (3) basic Informer (without WOA hyperparameter optimization). All models are trained and tested under the same generalized load dataset, and the performance results are shown in

Table 3. Forecasting performance comparison of different models.

Model	RMSE (MW)	MAE (MW)	MAPE (%)
ARIMA	2.386	1.872	8.62
LSTM	1.527	1.105	5.18
Basic Informer	1.063	0.784	3.65
GNG-Informer-WOA (Proposed)	0.682	0.497	2.13

.

The comparison results show that the proposed GNG-Informer-WOA model has the best prediction performance, with RMSE reduced by 71.4% compared with ARIMA, 55.3% compared with LSTM, and 35.8% compared with basic Informer. The GNG clustering reduces the complexity of load modeling by classifying typical load patterns, and WOA optimization effectively improves the prediction accuracy of the Informer model, fully verifying the effectiveness of the proposed model.

3. Distribution Network Operation Risk Assessment Index System

A scientific and comprehensive risk assessment index system is the foundation for accurate quantitative assessment of distribution network operation risks. The traditional index system cannot adapt to the new operational characteristics of distribution networks with high-proportion generalized load access, and it is difficult to fully reflect the potential operation risks of a system. To address this problem, this section constructs a multi-dimensional operation risk assessment index system for a new-type distribution network. This section will first introduce the general expression of distribution network operation risk, elaborate the construction logic of the index system, and finally give the definition and calculation formula of each sub-index for three dimensions, including voltage out-of-limit risk, regulation capacity risk and new energy consumption risk.

3.1. Establishment of Distribution Network Operation Risk Assessment Index System

The goal of the new distribution network operation risk assessment is to obtain an overall score and judge the operational state of the distribution network in a period of time.

The general expression of the operation risk of the new distribution network is shown in Equation (2).

$$Risk(X_{t,j})={\displaystyle \sum _{i}P(E_i)\times \left[{\displaystyle \sum _{n}P(\left.X_{t,n}\right|X_{t,j})}\times Sev(E_i,X_{t,n})\right]}$$

(2)

Here, t is the operation time of the distribution network (h), $X_{t,j}$ is the power grid operation mode at time; $X_{t,n}$ is the n-th possible system state; ${\displaystyle \sum _{n}P(\left.X_{t,n}\right|X_{t,j})}$ is the probability of the $X_{t,n}$ system state occurring under the $X_{t,j}$ operation mode; $E_i$ is the i-th anticipated uncertainty accident source; $P(E_i)$ is the probability of the occurrence of this uncertainty accident source; $Sev(E_i,X_{t,n})$ is the severity of the loss suffered by the system after the anticipated uncertainty accident source $E_i$ that occurs under the operating condition $X_{t,j}$.

The probability calculation of system states and uncertain events in the risk equations is based on quasi-Monte Carlo sampling with the Halton low-discrepancy sequence, which is used to generate sufficient and uniform operation scenarios of the distribution network. The specific calculation logic is as follows:

• Calculation of system state likelihood $P_n(t)$: Based on the generalized load output results obtained by the GNG-Informer-WOA model, we use the Halton low-discrepancy sequence to generate 500 groups of system operation samples (i.e., system states) within the 24 h assessment period. The likelihood of each system state $P_n(t)$ is determined by the frequency of the corresponding load scenario appearing in the sampling set, that is, $P_n(t)={\displaystyle \frac{N_n}{N_{total}}}$, where $N_n$ is the number of samples corresponding to the n-th system state, and $N_{total}=500$ is the total number of sampling samples. Compared with traditional Monte Carlo sampling, the Halton sequence has better uniformity and faster convergence, which can more accurately characterize the likelihood of system states with a smaller number of samples.
• Calculation of event probability $P_{a,i}$: For each uncertain risk event (e.g., voltage violation, power flow overload, line N-1 fault), the occurrence probability $P_{a,i}$ is calculated by the frequency of the event occurring in all sampling system states, that is, $P_{a,i}={\displaystyle \frac{N_{event}}{N_{total}}}$, where $N_{event}$ is the number of samples where the uncertain event occurs. For the 0–1 flag variables in each risk index, the value is 1 when the corresponding risk event occurs in the k-th sample, and 0 otherwise, which forms the basis for quantifying the occurrence probability of the risk event. The severity function $S_{n,i}(t)$ (and the severity functions in each sub-index) is constructed based on the relative deviation between the actual operating state and the safety threshold, which can quantitatively characterize the degree of system loss after the risk event occurs. The product of event probability and severity realizes the quantitative calculation of operational risk, which conforms to the classical probabilistic risk assessment theory of power systems.

The risk assessment indicators for the operation of the distribution network are analyzed from three aspects: the risk of distribution network voltage exceeding the limit, the risk of new energy consumption capacity, and the risk of distribution network regulation capacity. The specific structure is shown in Figure 3.

Based on the generalized load modeling method of the distribution network, the load results of each node in the distribution network are obtained, including voltage, active power, and reactive power. Each risk index is defined to comprehensively reflect the operation risk of the new distribution network.

3.2. Selection of Distribution Network Operation Risk Assessment Indexes

3.2.1. Distribution Network Voltage Violation Risk

(1)

Overvoltage Operation Risk

The overvoltage risk index reflects the risk that the voltage of each node in the distribution network exceeds the voltage upper limit under different system operation conditions. The probability of overvoltage and the operation risk are shown in Equation (3).

$$R_i^{vh}={\displaystyle \sum _{s\in \mathsf{\Omega }}{B}_{i,s}^{vh}(V_{i,s})Se{v}^{vh}(V_{i,s})}$$

(3)

Here, $R_i^{vh}$ is the overvoltage operation risk of the i-th node; $\mathsf{\Omega }$ is the set of generated operation cases; $B_{i,s}^{vh}$ is a 0–1 flag indicating whether overvoltage operation risk occurs; $V_{i,s}$ is the voltage of the node under the i-th case; $Se{v}^{vh}$ is the severity function of overvoltage above the upper limit, and the specific expression is shown in Equation (4).

$$Se{v}^{vh}\left(V_{i,s}\right)={\displaystyle \frac{V_{i,s}-V_{\max }}{V_{\max }-V_{\min }}}$$

(4)

Here, V_max = 1.07 pu.; V_min = 0.93 pu.

(2)

Low-voltage operation risk

The low-voltage risk index reflects the risk that the voltage is lower than the lower voltage limit under different system operating conditions. The probability of the voltage being closer to the lower limit and the risk of low-voltage operation at the node are shown in Equation (5).

$$R_i^{vl}={\displaystyle \sum _{s\in \mathsf{\Omega }}{B}_{i,s}^{vl}(V_{i,s})Se{v}^{vl}(V_{i,s})}$$

(5)

Here, $R_i^{vl}$ is the risk of low-voltage operation at a node; $B_{i,s}^{vl}$ is a 0–1 flag indicating whether low-voltage operation risk occurs; $Se{v}^{vl}$ is the severity function when the voltage does not reach the lower limit, as specifically shown in Equation (6).

$$Se{v}^{vl}(V_{i,s})={\displaystyle \frac{V_{\min }-V_{i,s}}{V_{\max }-V_{\min }}}$$

(6)

Here, V_max = 1.07 pu.; V_min = 0.93 pu.

3.2.2. Regulation Capacity Risk of the Distribution Network

(1)

Active Regulation Capacity Risk

The active power regulation ability refers to the active power regulation ability brought by the access to renewable energy. The calculation formula of the active power regulation ability of the distribution network is shown in Equation (7).

$$R^{PF}={\displaystyle \frac{n_1}{N}}$$

(7)

Here, R^PF is the risk of the active power regulation ability of the distribution network; $n_1$ is the number of lines in the distribution network for which the risk value cannot be zero, even when using all the active power regulation ability of a single line; N is the total number of distribution network lines.

(2)

Risk of reactive power regulation capability

Reactive power regulation capability refers to the reactive power regulation capability brought by renewable energy access. The calculation of reactive power regulation capability of the distribution network is shown in Equation (8):

$$R^{QF}={\displaystyle \frac{n_2}{N}}$$

(8)

Here, R^QF is the risk of reactive power regulation ability of the distribution network; $n_2$ is the number of lines in the distribution network, where the risk value of a single line cannot be zero, even if all the reactive power regulation capabilities of the single line are used.

(3)

N-1 contingency analysis

N-1 contingency analysis indicates the risk that each operation index of the system can still meet the given requirements after any one of the lines is disconnected. Its calculation formula is shown in Equation (9):

$$R^{N-1}={\displaystyle \frac{n_3}{N}}$$

(9)

Here, R^N−1 refers to distribution network N-1 risk; n₃ is the number of lines whose comprehensive risk is still increased after the use of regulation capacity when a single line in the distribution network fails.

3.2.3. Risk of New Energy Consumption Capacity

(1)

Risk of overloaded power flow operation

The risk of overloaded power flow characterizes the probability distribution and severity of the active power transmission volume of transmission lines exceeding their rated transmission capacity limits under different operating conditions. Its risk expression is shown in Equation (10).

$$R_j^p={\displaystyle \sum _{s\in \mathsf{\Omega }}{B}_{j,s}(P_{i,s})Se{v}^P(P_{i,s})}$$

(10)

Here, $R_j^p$ is the risk of overloading operation of the active power of the line; $B_{j,s}$ is a 0–1 flag indicating whether there is a risk of overloading operation of the power flow; $P_{i,s}$ is the active power flowing through the line under the case at moment; $Se{v}^{\mathrm{Pr}}$ is the severity function of power flow overload, and its expression is shown in Equation (11):

$$Se{v}^P(P_{i,s})={\displaystyle \frac{(P_{i,s}-0.7P_{i,\max })}{0.7P_{i,\max }}}$$

(11)

Here, $P_{i,\max }$ is the maximum power flow capacity.

(2)

Risk of reverse power flow overload operation

The output of the generalized load is volatile. When the output of the generalized load exceeds the absorption capacity of the distribution network, the reverse power flow of the distribution network is overloaded. Its risk expression is shown in Equation (12):

$$R_j^{pr}={\displaystyle \sum _{s\in \mathsf{\Omega }}{\rho }_s{B}_{j,s}^r(P_{i,s})Se{v}^{\mathrm{Pr}}(P_{i,s})}$$

(12)

Here, $R_j^{pr}$ is the risk of reverse power flow overload operation; $B_{j,s}^r$ is a 0–1 flag indicating whether there is a reverse power flow overload operation risk, marking whether a reverse power flow overload event occurs at the i-th case node; $P_{i,s}$ is the active power flowing through the line under the i-th case; $Se{v}^{\mathrm{Pr}}$ is the severity function of reverse power flow overload, specifically as shown in Equation (13):

$$Se{v}^{\mathrm{Pr}}(P_{i,s})={\displaystyle \frac{-P_{i,s}-0.7P_{i,\max }}{0.7P_{i,\max }}}$$

(13)

(3)

Risk of new energy output fluctuation

The risk of new energy output fluctuation refers to the adverse impact on the operation of the power system caused by the uncertainty of new energy power generation. Its risk expression is as shown in Equation (14):

$$R_g^{pv}={\displaystyle \sum _{s\in \mathsf{\Omega }}{B}_{g,s}^{r}Se{v}^{pv}(P_{i,s})}$$

(14)

Here, $R_g^{pv}$ is the fluctuation risk of new energy output; $B_{g,s}^r$ is a 0–1 flag indicating whether there is a fluctuation risk of new energy output; $Se{v}^{pv}(P_{i,s})$ is the severity function of new energy output fluctuation, specifically shown in Equation (15):

$$Se{v}^{pv}(P_{i,s})=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N(P_i-\mu )}}$$

(15)

Here, N is the number of samples; $P_i$ is the output at the i-th time point; $\mu$ is the average output.

4. Weight Setting of Distribution Network Operation Risk Assessment Indexes

The scientific determination of index weights is the core link to ensure the accuracy of distribution network operation risk assessment results. A single subjective or objective weighting method has inherent limitations, and it is difficult to balance the rationality of engineering experience and the objectivity of data characteristics. To solve this problem, this section proposes a game theory-based combined weighting method to calculate the weights of risk assessment indexes. This section will first introduce the basic principles of the AHP and PCA weighting methods, elaborate the implementation process of the game theory combined weighting method, and finally give the complete implementation process of the distribution network operation risk assessment method based on the proposed weighting method.

4.1. Analytic Hierarchy Process

The analytic hierarchy process (AHP) is a decision-making analysis method that combines quantitative analysis with qualitative analysis. Its basic principle is to break down complex decision-making problems layer by layer and construct a multi-level hierarchical structure model. AHP splits decision-making problems into multiple levels such as the goal level, criterion level, and alternative level.

The core of AHP is the construction of the judgment matrix. After hierarchical processing of the problem, the evaluation indicators are compared pairwise by the scale method and according to expert experience, and the ranking results of the weights of the evaluation indicators are obtained layer by layer, so as to obtain the judgment matrix. Constructing the judgment matrix and determining the relative importance between elements rely on the subjective judgment of decision-makers. This subjectivity may lead to certain deviations in the decision-making results and lack objectivity. Especially in the case of multiple decision-makers or inconsistent expert opinions, the differences in this subjective judgment may be further amplified, affecting the accuracy of decision-making. Therefore, in order to improve the objectivity and accuracy of the index weights and avoid the deviations caused by single subjective judgments, it is necessary to combine objective and scientific methods for determining index weights to correct and supplement the results of the analytic hierarchy process and obtain more comprehensive and reliable weights of the distribution network operation risk indicators.

Table 4. Scale values and meaning of 9-level scaling method.

Clustering	Number of Nodes
1	Xi is as equally important as Xj
3	Xi is slightly more important than Xj
5	Xi is significantly more important than Xj
7	Xi is strongly more important than Xj
9	Xi is extremely more important than Xj
2, 4, 6, 8	The importance is between 1, 3, 5, 7, and 9
Reciprocal of 1–9	Xi is more important than Xj and aij = 1/aij

displays the scale values and their meanings for the 9-level scaling method.

4.2. Principal Component Analysis Hierarchy Process

Although AHP can reflect the overall results of the evaluation system, it is centered around the evaluations of experts and is prone to overlooking objective facts, with subjective arbitrariness. Principal component analysis (PCA) can exactly make up for the defects of the subjective weighting method. It is an objective weighting method, and the index weight is equal to the normalization of the weighted average of the coefficients of the index in the linear combination of each principal component, with the variance contribution rate of the principal component as the weight.

When calculating the weights of the operating risk indicators of the distribution network, a combined weight that combines subjective and objective factors is adopted. By using the qualitative advantages of the analytic hierarchy process and the principal component analysis method, the actual situation can be considered more comprehensively and reasonably, which can eliminate the overlap between information and thus more accurately determine the weight coefficients of the indicator system. However, when the analytic hierarchy process and the principal component analysis method are used separately, there are differences in their respective weight results, and it is difficult to accurately measure the operating risk indicators of the distribution network by direct application. Therefore, the game theory method is introduced to integrate the two methods.

4.3. Game Theory Method

Game theory aims to minimize the differences between the weight vectors obtained by different methods, and combines constraints such as non-negativity and normalization of weights to obtain the weight coefficients of the operation risk index system of the distribution network that can comprehensively reflect the advantages of the two methods, so as to more accurately determine the index weights.

Under the framework of game theory, the combined weighting method regards the index weights determined by the analytic hierarchy process and the principal component analysis method as two participants in the game, and the optimal combined weight of this method is the weight combination formed by these two game parties when reaching a balanced state. This approach minimizes the deviation between the subjective weight W₁ and the objective weight W₂, that is, the minimum deviation method is used to determine the optimal combined weight. The specific steps are as follows:

(1) Calculate the combined weight matrix W represented by the linear combination of W₁ and W₂, as shown in Equation (16):

$$\mathrm{W}={\lambda }_1{W}_1^T+{\lambda }_2{W}_2^T$$

(16)

Here, ${\lambda }_1$ and ${\lambda }_2$ are the linear combination coefficients.

(2) Optimize the linear combination coefficients in Equation (16) to minimize the deviation of the optimized W₁ and W₂, with the objective function and constraints, as shown in Equation (17):

$$\min {‖{\displaystyle \sum _{k=1}^2{\lambda }_k}{W}_k^T-W_v^{\mathrm{T}}‖}_2, v=1,2$$

(17)

(3) Derive the optimal first-order derivative of the above formula according to the differential properties of the matrix, as shown in Equation (18):

$$\left[\begin{array}{cc}{W}_1{W}_1^T& W_1{W}_2^T\\ W_2{W}_1^T& W_2{W}_2^T\end{array}\right]\left[\begin{array}{c}{\lambda }_1\\ {\lambda }_2\end{array}\right]=\left[\begin{array}{c}{W}_1{W}_1^T\\ W_2{W}_2^T\end{array}\right]$$

(18)

Normalize the obtained linear combination coefficients λ₁ and λ₂, as shown in Equation (19):

$$\left\{\begin{array}{l}{\lambda }_1^{*}={\displaystyle \frac{\left|{\lambda }_1\right|}{\left|{\lambda }_1\right|+\left|{\lambda }_2\right|}}\\ {\lambda }_2^{*}={\displaystyle \frac{\left|{\lambda }_2\right|}{\left|{\lambda }_1\right|+\left|{\lambda }_2\right|}}\end{array}\right.$$

(19)

Finally, the optimal combined weights of the evaluation indexes are shown in Equation (20):

$${\mathrm{W}}^{*}={\lambda }_1^{*}{W}_1^T+{\lambda }_2^{*}{W}_2^T$$

(20)

The calculation process of the weights of operation risk assessment indicators is shown in Figure 4.

4.4. Operation Risk Assessment Method of Distribution Networks Based on Generalized Load Game Theory Method

To comprehensively evaluate the operation risks of new distribution networks under different load access cases, in this section, five types of risk cases are constructed: (1) only traditional loads are connected; (2) only distributed wind power is connected; (3) only distributed photovoltaic is connected; (4) only distributed energy storage is connected; and (5) distributed wind power, photovoltaic and energy storage are connected simultaneously.

Based on the proposed generalized load modeling method for the distribution network, the load results under five typical cases are solved. With the help of the Halton low-discrepancy sequence, more uniform case samples are generated and used as the input for the operation risk assessment.

Finally, the analytic hierarchy process and the principal component analysis are integrated, and game theory is introduced to accurately calculate the weights of the risk indicators. Finally, the comprehensive operation risk of the distribution network is quantified. The schematic diagram of this assessment is shown in Figure 5.

Figure 5 shows the complete closed-loop process of the distribution network operation risk assessment method proposed in this paper, which realizes the full chain from generalized load data input to comprehensive risk quantification output. The method first realizes the accurate characterization of the uncertainty source of the distribution network through the GNG-Informer-WOA generalized load modeling method, and then generates uniform and sufficient operation scenario samples through the Halton low-discrepancy sequence, which solves the problems of slow convergence and poor uniformity of the traditional Monte Carlo sampling method. On this basis, the three-dimensional risk index system constructed in this paper is used to realize the multi-dimensional characterization of operation risks, and the game theory combined weighting method is used to balance the subjective expert experience and objective data characteristics, so as to realize the accurate quantitative assessment of the comprehensive operation risk of the distribution network. This standardized assessment process provides a unified implementation framework for the multi-scenario risk comparison and verification in the subsequent case study.

5. Case Studies

To verify the feasibility of the proposed method, five types of risk cases are constructed. The risk assessment period is set to 24 h. The Halton low-discrepancy sequence is used to generate case samples, and the number of samples is 500. The five types of case load results obtained based on the generalized load modeling method are used as the input data set for operation risk assessment. Combining the proposed distribution network operation risk indicators and the proposed weight calculation method, the quantitative assessment of the new distribution network operation risk is realized. Finally, the reference threshold table of the distribution network operation risk is shown in Table 2. Figure 6 shows a 33-node distribution network model.

The following

Table 5. Reference threshold table for distribution network operation risks.

Risk Level	Degree of Risk	Risk Threshold
Normal	Low risk	[0, 35)
Alarm	Medium risk	[35, 70)
Emergency	Severe risk	[70, 100)

shows the reference threshold for distribution network risks.

(1)

Case 1 (Only traditional load access, comprehensive risk value 17.888, normal level)

The traditional distribution network without generalized load access has the lowest operational risk, with all sub-indexes at a low level. The main risk comes from a small amount of low-voltage risk at the end of the line during peak load periods, while regulation capacity risk and new energy consumption risk are almost zero. Core inference: The traditional distribution network has a mature operation mode and sufficient regulation margin. Its operational risk is mainly determined by the peak–valley difference in conventional load, with a stable and controllable risk level, and can maintain long-term normal operation. The specific risk assessment results are shown in Figure 7.

(2)

Case 2 (Addition of only distributed wind power, comprehensive risk value 47.180, Alarm level)

With the addition of wind power, the comprehensive risk increases by 163.8% compared with Case 1. The main risk sources are: new energy output fluctuation risk (weight proportion 32.1%), reverse power flow overload risk (28.6%), and voltage over-limit risk (21.3%). The active regulation capacity risk also increases significantly, as the random fluctuation in wind power output leads to frequent reverse power flow, requiring frequent adjustment of reactive power compensation devices. Core inference: The strong randomness of wind power output is the core source of operational risk. Reverse power flow caused by wind power grid connection will lead to over-limit voltage at the grid connection point, which is the key risk point to be focused on in distribution networks with high-permeability wind power access. The specific risk assessment results are shown in Figure 7.

(3)

Case 3 (Addition of only distributed photovoltaics, comprehensive risk value 38.625, Alarm level)

With the addition of photovoltaics, the comprehensive risk increases by 115.9% compared with Case 1, which is lower than Case 2. The main risk sources are: new energy output fluctuation risk (29.4%), over-limit voltage risk (26.8%), and power flow overload risk (22.1%). Compared with wind power, photovoltaic output has obvious diurnal regularity and smaller daytime fluctuation, so the risk level is lower; over-limit voltage risk is mainly concentrated in the noon period, which has the highest photovoltaic output. Core inference: The operational risk of photovoltaic access is mainly concentrated in the peak output period, and its risk is more predictable than wind power. Grid operators can carry out pre-regulation according to photovoltaic output forecast to reduce over-limit voltage risk. The specific risk assessment results are shown in Figure 8.

(4)

Case 4 (Addition of only distributed energy storage, comprehensive risk value 42.357, Alarm level)

With the addition of energy storage, the comprehensive risk increases by 136.8% compared with Case 1. The main risk source is N-1 contingency risk (weight proportion 41.2%), followed by active and reactive regulation capacity risk (35.7%). Over-limit voltage risk and power flow risk are at a low level, as energy storage can smooth load fluctuation. Core inference: Although energy storage can suppress voltage and power flow fluctuation caused by load changes, the charge–discharge scheduling of energy storage changes the system power flow distribution, reducing the N-1 safety margin of lines. The operation risk of energy storage access mainly comes from the complexity of scheduling strategy, and it is necessary to optimize the charge–discharge plan of energy storage to ensure the N-1 safety of the system. The specific risk assessment results are shown in Figure 8.

(5)

Case 5 (Simultaneous accessing of multiple generalized loads, comprehensive risk value 64.166, Alarm level, close to Emergency threshold)

With the combined access to wind power, photovoltaic and energy storage, the comprehensive risk reaches the highest level, 258.7% higher than Case 1. All sub-indexes are at a high level, among which regulation capacity risk (30.2%), new energy output fluctuation risk (28.5%), and over-limit voltage risk (24.7%), are the three highest risk sources. The superposition of wind and photovoltaic output fluctuations leads to more frequent power flow reversal, and the coupling of energy storage charge–discharge scheduling further reduces the system regulation margin. Core inference: The combined accessing of multiple generalized loads will lead to the superposition and coupling of various risk sources, which is the most dangerous operation scenario for new-type distribution networks. The risk level is close to the Emergency threshold, and grid operators need to carry out real-time monitoring and active control to avoid the risk further rising to the Emergency level. The specific risk assessment results are shown in Figure 9.

Traditional load-only access (Case 1) has the lowest risk, indicating stable operation of traditional distribution networks; new energy access (Cases 2–3) increases risk due to output volatility: wind power (Case 2) has higher risk than photovoltaic power (Case 3) because wind speed is more random; energy storage access (Case 4) leads to medium risk, with prominent N-1 contingency risk due to complex charge–discharge scheduling; combined accessing of multiple generalized loads (Case 5) results in the highest risk: the superposition of wind/photovoltaic volatility and energy storage scheduling complexity exacerbates regulation difficulty and power flow imbalance, significantly increasing operational risk.

Based on these risk assessment results and the set risk level thresholds, we propose targeted mitigation strategies for different risk levels, and clarify how grid operators can use the risk scores to trigger control actions to restore a system to its normal state.

• Normal level (risk value 0–35)

For low-risk scenarios, grid operators mainly adopt preventive control strategies: maintain the conventional operation mode, carry out regular equipment inspection, and update the generalized load prediction model regularly to ensure the accuracy of risk assessment. No additional control action is required, and the system can maintain stable operation.

2.

Alarm level (risk value 35–70, e.g., Cases 2, 3, 4, 5)

When the risk score enters the Alarm level, grid operators should trigger active regulation control actions immediately to prevent the risk from further rising to the Emergency level. Specific mitigation strategies are formulated according to the main risk sources:

If the main risk source is over-limit voltage, operators should trigger the on-load tap changer (OLTC) of the distribution transformer, switch the reactive power compensation capacitor bank, and adjust the reactive power output of renewable energy and energy storage to restore the node voltage to the allowable range.

If the main risk source is power flow overload/reverse power flow, operators should optimize the charge–discharge plan of energy storage, smooth the output fluctuation of renewable energy through energy storage, and curtail part of the renewable energy output in severe cases to eliminate reverse power flow overload.

If the main risk source is insufficient regulation capacity/N-1 risk, operators should adjust the grid operation topology, transfer the load of heavy-load lines to light-load lines, and optimize the active power output of each distributed power source to improve the N-1 safety margin of the system.

For Case 5 (risk value 64.166, close to the Emergency threshold), the priority is to suppress the output fluctuation of wind and photovoltaic power through energy storage, optimize the reactive power output of each grid-connected node to eliminate over-limit voltage, and check the N-1 safety of each line to avoid cascading failures.

3.

Emergency level (risk value 70–100)

When the risk score enters the Emergency level, grid operators should trigger emergency control strategies immediately to avoid large-scale power outages. Specific actions are as follows. Operators should quickly cut off the faulty line through the circuit breaker, execute the load shedding plan for non-important loads, limit the output of renewable energy in the fault area, and start the standby power supply, to quickly reduce the risk level and restore the system to a safe operation state.

6. Conclusions

This paper focuses on the generalized load modeling and operation risk assessment of new-type distribution networks with high-proportion generalized load access, and proposes a complete set of distribution network operation risk assessment methods based on generalized load modeling, which provides technical support for the safe and stable operation of new-type distribution networks.

In terms of generalized load modeling, this paper proposes a GNG-Informer-WOA fusion non-mechanistic modeling method. The GNG algorithm is used to realize adaptive clustering of load curves and noise data identification, which solves the problem that traditional clustering algorithms need to pre-set the number of clusters and are sensitive to noise. The WOA-optimized Informer model is used to realize high-precision prediction of generalized load characteristics, which effectively captures the long-sequence time-series dependence of generalized load, and provides high-confidence input data for risk assessment.

In terms of risk assessment system construction, this paper constructs a three-dimensional operation risk assessment index system covering voltage out-of-limit risk, regulation capacity risk and new energy consumption risk, which fully considers the operation characteristics of a distribution network under generalized load access, and realizes the comprehensive characterization of multi-dimensional operation risks of the system. Aiming to overcome the limitations of a single weighting method, this paper introduces game theory to fuse AHP and PCA, realizing the complementary advantages of subjective and objective weighting methods, and ensures the validity and accuracy of index weight calculation.

The case study based on the improved IEEE 33-bus system verifies the effectiveness of the proposed method. The results are as follows: A traditional distribution network with only traditional load access has the lowest comprehensive operation risk, with a risk value of 17.888, which is in the low-risk normal operation state. Accessing new energy (wind power and photovoltaics) will significantly increase the operation risk of the distribution network, and the risk of wind power access is higher than that of photovoltaics access due to the stronger randomness of wind speed. Accessing energy storage will bring medium operation risk, and the N-1 contingency risk is prominent due to the complexity of charge–discharge scheduling. The combined accessing of multiple generalized loads has the highest comprehensive risk, with a risk value of 64.166, which is in the medium-risk alarm state. The superposition of the volatility of wind power and photovoltaics, and the complexity of energy storage scheduling exacerbate the difficulty of system regulation and power flow imbalance, which are the core source of operation risk. The proposed method can effectively characterize the characteristics of generalized load and accurately quantify the operation risk of the distribution network under different scenarios.

The proposed method can provide a scientific decision-making basis for operation scheduling, risk early warnings and optimal control of the new-type distribution networks, and has strong engineering application value. In future research, we will further optimize the generalized load modeling method, consider the coupling characteristics of source–grid–load–storage in the distribution network, and expand the risk assessment index system to cover the cyber security risks to distribution networks under the background of digitalization. In addition, we will embed the proposed risk assessment method into actual distribution network operation control systems, and carry out engineering application verification based on the actual operation data of distribution networks to further improve the engineering practicability of the method.