SVM finds extensive use in pattern recognition, data classification, and regression analysis. Nonetheless, SVM’s performance is somewhat reliant on parameters, necessitating an improvement to enhance its operational and risk-detection capabilities. This study thus proposes to enhance SVM using LSA. Additionally, a power network security risk evaluation model is developed, grounded in LSA-SVM, to assess and forecast power system security risk. The work combines the LSA algorithm and the SVM algorithm to increase the accuracy and computing speed of the standard PNSREM, and therefore creates the improved PNSREM for the assessment of PN security risk. Firstly, the study constructs the PN security risk indicator system, and then uses the LSA algorithm to improve the SVM algorithm. Then, the risk is classified and predicted by the LSA-SVM algorithm, so as to construct the PNSREM based on the LSA-SVM algorithm.
SRAIS construction of PCN
PCN is a key infrastructure in PSs, which is responsible for realising the communication and data transmission functions of PSs, and is crucial for the operation and management of PSs. However, as information technology advances and PCN intelligence improves, PCNs are exposed to an increasing number of security threats22,23. As a result, it is critical to develop a scientific and acceptable SRAIS for PCNs in order to assure the safe operation of PCNs. To begin, defining the characteristics and security requirements of PCN is the foundation for developing security risk assessment indices. As an important part of PS, the main task of PCN is to transmit and manage various information in PS. Therefore, SRAIS should be considered in terms of scientific, systematic, generic, practical and independent, and the SRAIS of PCN is constructed with this principle. The construction steps of this system are shown in Fig. 1.
Construction steps of electric power network security risk assessment index system.
In Fig. 1, the experiment will select preliminary PN security risk evaluation indicators based on a large amount of existing literature and the principles of indicator construction24,25. Due to the huge amount of information, to ensure the comprehensiveness of the evaluation indicators, the preliminary selection of evaluation indicators is prone to the problem of huge number, which in turn leads to the distortion of the evaluation results. Therefore, the study will use the weighted judgement method to screen these indicators. The weight judgement method is a commonly used method to determine the importance of each indicator in the whole indicator system by assigning weights to it. The study will rely on expert ratings as the basis of weights, and determine the weight value of each indicator through the experience and knowledge of the experts. The calculation equation of the weight judgement method is shown in Eq. (1).
$$ f_{i} = \left\{ {\begin{array}{*{20}l} {\lambda_{i} > \lambda_{ch} ,} \hfill & {Sieve \, extraction} \hfill \\ {\lambda_{i} \ge \lambda_{ch} ,} \hfill & {Sieve \, off} \hfill \\ \end{array} } \right. $$
(1)
In Eq. (1), \(f_{i}\) denotes the \(i\)th evaluation indicator; \(\lambda_{i}\) denotes the weight of \(f_{i}\); and \(\lambda_{ch}\) denotes the screening weight. Subsequently, the study verified the validity of the screened indicators based on the expert scores to ensure that the screened indicators objectively reflect the security risk of the PN. In the validity validation process, the study uses the validity coefficient to assess the correlation between the screened indicators and the security risk of the PN. The equation for calculating the validity coefficient is shown in Eq. (2).
$$ \beta_{i} = \sum\limits_{j = 1}^{n} {\left| {\overline{{x_{i} }} – x_{ij} } \right|} /S*M $$
(2)
In Eq. (2), \(\beta_{i}\) denotes the validity coefficient of \(f_{i}\); \(\overline{{x_{i} }}\) denotes the average of the expert ratings of \(f_{i}\); \(x_{ij}\) denotes the rating of \(f_{i}\) by the \(j\)th expert; \(S\) denotes the number of experts; and \(M\) denotes the optimal value of the rating. By calculating the validity coefficients, the study was able to determine the predictive ability of each risk assessment indicator for assessing the security risk of PN. In addition to this, the study also assessed the reliability and consistency of the screened indicators through the reliability coefficient. The study calculates the reliability coefficient through multiple assessments and the participation of different experts to ensure that the screened indicators can maintain stable assessment results under different circumstances. Equation (3) shows how to compute the dependability coefficient.
$$ \rho_{i} = \sum\limits_{j = 1}^{n} {\frac{{\sum\limits_{i = 1}^{n} {(x_{ij} – \overline{{x_{j} }} )} (y_{i} – \overline{y} )}}{{\sqrt {\sum\limits_{i = 1}^{n} {(x_{ij} – \overline{{x_{j} }} )^{2} \sum\limits_{i = 1}^{n} {(y_{i} – \overline{y} )^{2} } } } }}} /S $$
(3)
In Eq. (3), \(y_{i}\) represents the average data of the expert ratings of the \(S\) times of calculation; the overall mean of the \(\overline{y}\) average data. Through the validation of validity and reliability, the study can make timely amendments and deletions to the indicator system to ensure the validity and reliability of the PN security risk evaluation indicator system. Only a strictly screened and verified indicator system can more accurately assess the security risk of PN, provide scientific and reliable decision-making basis for relevant departments, and guarantee the stable operation of PN. Table 1 depicts the PN security risk evaluation index system developed by the study.
As can be seen from Table 1, the study looks at six dimensions of PNs: topology, access control function, authentication function, security vulnerability, data backup and recovery, and data transmission encryption. Quantitative analysis and qualitative assessment methods can be used and combined with the actual situation for a comprehensive assessment. Such an assessment helps to equationte appropriate security measures and contingency plans to improve the security and reliability of PNs. According to the key facilities of the power system and the method of the power grid security risk evaluation index, the power grid security risk evaluation system is developed and designed, which provides the index basis for the security risk evaluation algorithm.
construction of PN security risk evaluation algorithm
SVM is a commonly used machine learning algorithm for performing classification and regression tasks, with good handling of high-dimensional feature spaces and small-sample data, as well as non-linear problems26,27.The support vector machine (SVM) offers robustness, adaptability and high efficiency when tackling nonlinear issues, making it commonly applied in assessing security risks in network systems. However, SVM has limitations; the abundance of data in power networks can result in high calculations costs if solely usedfor risk assessment. Furthermore, the effectiveness of Support Vector Machines (SVM) in power network security risk evaluation heavily relies on the careful selection of parameters. Thus, it is crucial to enhance the performance of SVM by utilizing optimization algorithms, which can boost accuracy and reliability. SVM operatesby converting low-dimensional space data into high-dimensional space through vector mapping.The principle of SVM vector mapping is shown in Fig. 2.
The SVM vector mapping principle.
SVM maps the samples into the high-dimensional feature space, as illustrated in Fig. 2, so that the samples are divided by feature space hyperplanes, as given in Eq. (4).
$$ f(x) = b + \omega \varphi (x) $$
(4)
In Eq. (4), \(\omega\) denotes the weights in the high-dimensional space; \(\varphi ()\) denotes the mapping process; \(x\) denotes the input sample vector; and \(b\) denotes the regression bias item. The equation of the risk function is shown in Eq. (5).
$$ R(\omega ) = \frac{1}{2}\left\| \omega \right\|^{2} + C\sum\limits_{i = 1}^{n} {l( – y_{i} + f(x_{i} ))} $$
(5)
In Eq. (5), \(C\) denotes the penalty factor; \(y_{i}\) denotes the mapping vector; \(l()\) denotes the high-dimensional mapping. In order to minimise the structural risk, it is investigated to control the accuracy of SVM by linear non-sensitive mapping, which is calculated as shown in Eq. (6).
$$ \max (0,\left| { – y_{i} + f(x_{i} )} \right| – \varepsilon ) = l(f(x_{i} ) – y_{i} ) $$
(6)
In Eq. (6), \(\varepsilon\) denotes the insensitive parameter. The study transforms the regression problem into a dyadic problem by adding operators to the function and based on the Lagrangian dyadic theory, which is shown in Eq. (7).
$$ \left\{ {\begin{array}{*{20}c} {\max L(a) = \sum\limits_{i = 1}^{n} {(a_{i} – a_{i}^{*} )y_{i} – } \frac{1}{2}\sum\limits_{i,j = 1}^{n} {(a_{j} – a_{j}^{*} )(a_{i} – a_{i}^{*} )K(x_{i} ,x_{j} ) – } \sum\limits_{i = 1}^{n} {(a_{i}^{*} + a_{i} )\varepsilon } } \\ {s.t.\sum\limits_{i = 1}^{n} {( – a_{i}^{*} + a_{i} ) = 0,a_{i} a_{i}^{*} \in [0,C]} } \\ \end{array} } \right. $$
(7)
In Eq. (7), \(K()\) denotes Lagrange multiplier; \(a\) and \(a^{*}\) denote Lagrange multipliers. When any one of the Lagrange multipliers is not 0, the variables in the sample become support vectors at this time, and the equation is shown in Eq. (8).
$$ K(x_{i} ,x) = e^{{ – \gamma \left\| {x_{i} – x} \right\|^{2} }} $$
(8)
In Eq. (8), \(\gamma\) denotes the kernel function parameters. Equation (9) depicts the choice function’s equation.
$$ f(x) = \sum\limits_{i = 1}^{n} {(\alpha_{i} – \alpha_{i}^{*} )e^{{ – \gamma \left\| {x_{i} – x} \right\|^{2} }} + b} $$
(9)
Combining the above descriptions, it can be seen that the accuracy performance, robustness performance and generalisation performance of SVM depend on the insensitivity coefficient and penalty factor of SVM. Therefore, in order to quickly select the optimal parameters of SVM, improve the performance of SVM, and accelerate the training speed of SVM. The study will improve the SVM based on LSA and construct the LSA-SVMPN security risk evaluation algorithm, which is a heuristic search algorithm commonly used in solving combinatorial optimisation problems, with global search capability and high convergence speed.Theoperational steps of the LSA algorithm simulate the behaviour of lightning as it searches for the shortest paths through the cloud layer. It does this by randomly generating a set of solutions, i.e. discharges, in the search space and then updating the discharges according to the fitness of each discharge. The LSA controls the search process based on the location of the current optimal solution and the global ideal solution, while injecting some randomisation to avoid slipping into the local optimal solution.The implementation flow of the LSA is shown in Fig. 3.
Implementation process of the LSA.
As shown in Fig. 3, the discharging body is one of the core concepts of LSA. In the cloud, the discharging body loses kinetic energy when it elastically collides with other particles, and the velocity equation in this process is given by Eq. (10).
$$ v_{p} = 1/\sqrt {\left[ {1 – (1/\sqrt {\left( {1 – v_{0} /c} \right)^{2} – sF_{i} /mc^{2} } )^{ – 2} } \right]} $$
(10)
In Eq. (10), \(v_{0}\) denotes the initial velocity of the discharger; \(m\) is the mass of the discharger; \(s\) is the motion distance of the discharger after the collision; \(c\) is a constant, i.e., the speed of light; and \(F_{i}\) is the ionisation rate constant.In the LSA, in addition to the exploration of the target solution space achieved by collision, the discharger can also generate a new branch through the creation of a symmetric path. At this time the new discharge body creation process is shown in Eq. (11).
$$ \overline{{p_{i} }} = h + h^{\prime} – p_{i} $$
(11)
In Eq. (11), \(\overline{{p_{i} }}\) and \(p_{i}\) are the two newly generated dischargers, respectively; \(h\) and \(h^{\prime}\) are the boundary limits of the solution space. In the LSA algorithm, the dischargers are divided into three kinds of dischargers, which are transition dischargers, spatial dischargers and guided dischargers. Among them, the transition discharger can be particleinitialized for LSA, and the spatial discharger is created by using the standard uniformly distributed probability function. And the spatial discharger selects the optimal solution to the space by changing the position of the discharger, which will move the distance to the space. When the maximum number of iterations has been reached andthere are no more optimal solutions, the optimal solution selected at that time becomes the guided discharge body. The equation for the normal probability density function of the lead body is given by Eq. (12).
$$ f(x^{L} ) = \frac{1}{{\sigma \sqrt {2\pi } }}e^{{ – (x^{L} – \mu )^{2} /2\sigma^{2} }} $$
(12)
In Eq. (12), \(x^{L}\) denotes the guided discharge body; \(\sigma\) is the scale parameter; \(\mu\) is the shape parameter. To avoid slipping into the local optimal solution, it is investigated to introduce a certain degree of randomization in the rows of the LSA, as indicated in Eq. (13).
$$ P_{i – new}^{L} = P_{i}^{L} \pm norm(rand(\mu_{L} ,\sigma_{L} )) $$
(13)
In Eq. (13), \(rand(\mu_{L} ,\sigma_{L} )\) denotes the random shape parameter and size parameter; \(P^{L}\) is the position of the bootstrap discharger; \(norm()\) denotes the normal distribution function. In order to construct the LSA-SVMPN security risk assessment algorithm, firstly, the study replaces the parameters of the support vector regression machine with the discharge bodies in the LSA and assigns initial energy to each discharge body. The study then uses LSA to optimise the diffusers to find the optimal diffuser positions. The study then assigns the position coordinates of the discharge bodies to the parameters of the support vector regression machine as parameter values. Finally, the study uses the obtained parameters to train the SVM to assess the PN security risk, resulting in the final LSA-SVMPN security risk assessment method. Figure 4 depicts the implementation flow of the LSA-SVM method developed in the study.
Implementation process of the LSA-SVM algorithm.
As shown in Fig. 4. The LSA-SVM risk evaluation algorithm constructed in the study is divided into two modules, i.e., the LSA optimal parameter selection module and the SVM security risk assessment module. In the LSA Optimal Parameter Selection module, the study replaces the parameters to be optimised in the SVM with the discharge body in the LSA and initialises the initial parameters of the LSA and SVM. For example, the high-dimensional space weights, the initial energy of the discharge body and the maximum number of iterations. The fitting evaluation phase is then entered. The study evaluates the fitness of all input dischargers. If the initial energy of this discharger is sufficient to complete the exploration of the spatial solution, the symmetric channel is generated and the new space is reached by selecting the channel with higher energy among them. Otherwise, the original energy is used to create a new room discharger and reach the new room. The guided discharger is output as the best option if, when the maximum number of iterations is reached, there is no guided discharger with a higher adaptation value. This is the third and final step. The SVM security risk evaluation stage is started after the optimal parameter selection is completed. After collecting the PN security data, the study takes the network security data as the input training data and preprocesses this data to improve the training efficiency and training speed. The study optimises the penalty factor and insensitive parameters of SVM using LSA in the first module to achieve the ideal parameters. To finish SVM training, the optimal parameters are entered into SVM. Finally, the outcomes of the PN security risk evaluation. The LSA and SVM are effectively integrated and optimized according to the LSA parameter module and the SVM vector mapping. It then provides algorithm guidance for the power grid security risk assessment model.
PNSREM based on LSA-SVM algorithm
PNSREM is a model used to assess the security and risk level of a PCN system. It can assess the security risk of a PN in a quantitative or qualitative manner by collecting, analysing and processing relevant data of the PCN system, and considering various potential security threats and risk factors in a comprehensive manner.The main functional modules of the PN Security Risk Evaluation Model (PNSREM) are shown in Fig. 5.
Functional module of the power network security risk assessment model.
A data collection module, a security threat identification module, a security threat analysis module, a risk assessment module, a risk detection module, a risk warning module and a data processing module are the main components of the PN risk security assessment model, as shown in Fig. 5. Among them, the data collection and processing module is mainly responsible for collecting various PCN system data, such as network topology, device status, communication traffic, etc., and processing and preparing the data for further analysis and evaluation. The security threat identification and analysis module, on the other hand, identifies and analyses possible security threats in the PCN system, such as network attacks, malware, information leakage, etc., in order to identify potential security risks. On the other hand, the risk assessment module assesses the security risk of the PN based on the results of the identification and analysis of security threats and the characteristics and requirements of the PN network. This is done using quantitative or qualitative approaches. The result of the assessment is the PN Security Risk Evaluation Index constructed by the study. After completing the analysis and output of PN risks, the risk monitoring and alerting module then conducts real-time monitoring of the security status of the PN to detect abnormal behavior and potential threats to the network in a timely manner and provide early warning to network maintenance personnel so that they can take timely and appropriate security measures and coping strategies to reduce losses due to the impairment of network function. Finally, the PN Security Fengxia Evaluation Module can also store historical data and provide intuitive graphs, reports and other forms in a visual display interface to make it easier for PS managers to understand and analyze the security risk situation of the PCN system. To achieve the above functions, the study integrates the LSA-SVM evaluation algorithm with the PNSREM and constructs the PNSREM based on the LSA-SVM.The evaluation function implementation flow of the model is entered into Fig. 6.
The evaluation process of the power network security risk evaluation model based on LSA-SVM.
The implementation of the security risk evaluation function is broken down into seven parts, as shown in Fig. 6. The study’s first phase is data collecting, which can be accomplished by requesting information from power companies, regulatory bodies, academic institutions, and other sources about PN security. The collected data comprise power system topology, equipment specifications, fault records, historical incident reports, and related information. Following this initial phase, the data undergo preprocessing to streamline calculations, promote efficiency, and minimise errors. This involves essential operations such as data cleaning, noise reduction, and data normalisation. Ensure the accuracy and consistency of the data. The third step is feature extraction of the preprocessed data using LSA-SVM algorithm, the study selects and extracts suitable features to describe the security status and risk factors of PN, such as current, voltage, frequency, load and other related indicators, according to the goal of security risk evaluation.The fourth step is label generation, where the study generates two types of labels, security and risk, for the data samples based on historical accident and failure records in order to train and evaluate the model. The fifth step is the training of the pair of features and labels using the LSA-SVM algorithm. During the training process, LSA-SVM constructs a decision boundary capable of separating normal and fault states based on the features and labels of the training samples. The sixth step is model evaluation and performance optimisation, where the study evaluates the trained model using a test set and calculates the model’s accuracy, recall and other metrics on identifying normal and fault states. Based on the evaluation results, the model is optimised and tuned to further improve its evaluation performance. In the final step for using this SREM in real scenarios, it is investigated to classify and evaluate PN security data using the trained ISA-SVM model. Based on the output data from this model, the research may assess the PS’s current level of security and potential dangers, and it can also offer support for security management and PS operation. Through the above steps, the IAS-SVM-based PNSREM can achieve the assessment and prediction of PS security risks, and help power operators and decision makers to identify potential security risks in time and take appropriate measures to ensure the safe operation of PSs.
