Identifying topology of distribution substation in power Internet of Things using dynamic voltage load fluctuation flow analysis

IoT and PIoT

The IoT constitutes a network facilitating information exchange among objects and individuals over the internet. It has emerged as a prominent focal point in the next generation of the information revolution, garnering worldwide attention (Chan et al., 2019; Park, Lee & Choi, 2019). Its applications span a wide array of domains, including smart cities, intelligent transportation, and telemedicine. Within this spectrum, IoT’s integration in the realm of electrical power, as a significant branch of IoT, assumes a pivotal role within power systems (Wang et al., 2021). The IoT architecture is shown in Fig. 1.

PIoT interconnects diverse electrical devices and personnel within the power system using information sensing devices. It amalgamates network information technology, electronics, and artificial intelligence to augment the reliability, efficiency, and intelligence of the power grid (Sharma et al., 2021; Aguilera, Ortiz & Ortiz, 2021). For example, PIoT facilitates applications such as smart power services, energy efficiency management, and intelligent home control, offering users a more user-friendly electricity experience. Moreover, it enhances load balancing and increases energy resource utilization efficiency within the power system (Rodrigues et al., 2022). These practical illustrations underscore the significance and potential advantages of the PIoT in power systems. A comprehensive PIoT encompasses communication transmission technology, information processing, big data technology, cloud computing, and various data management technologies, thereby evolving into an intricate intelligent network ecosystem (Pang, 2020). The overarching framework of the PIoT is depicted in Fig. 2.

Figure 2 illustrates the architectural framework of the PIoT, comprising five interconnected components: transmission links (including line monitoring and video surveillance), PIoT, power lines (for remote meter reading), distribution systems (enabling distribution automation), and substations (facilitating equipment maintenance). At the core of the PIoT architecture lies network communication technology, which serves as the foundational infrastructure for transmitting and communicating sensor monitoring data. Network communication technology establishes connections between sensor devices, whether through wireless or wired networks, facilitating the transfer of sensed information to the PIoT. The PIoT assumes the pivotal role of a central hub for data aggregation and processing. It meticulously gathers and manages data originating from various sensors and devices, thereby offering real-time monitoring and vital support for power system operation and management. Leveraging advanced data processing and analysis techniques, the PIoT processes sensor monitoring data, enabling real-time monitoring, analysis, and diagnostics. This capability empowers the extraction of valuable insights and information, subsequently underpinning decision-making processes and operational management within the power system.

The electronic information system of the PIoT encompasses a variety of technologies drawn from diverse domains. These technologies frequently manifest in unique technical configurations and application specifications across various industries. Figure 3 elucidates the architectural model of PIoT technology through four distinct modules (Mabrouki et al., 2021; Sharma, Sharma & Ahlawat, 2021).

Figure 3 comprises four pivotal modules: perception and identification technology, network and communication technology (Yang & Wang, 2021; Martins et al., 2021), computing and service technology, and management and support technology (Chen et al., 2021; Paudel & Neupane, 2021). These modules assume critical roles in the system’s functionality and operational dynamics.

Voltage correlation based on time series analysis

Voltage correlation is widely utilized in time series analysis as a crucial quantitative measure for determining power system topologies. The fundamental principle of voltage correlation can be understood as follows: Voltage drop occurs when current flows through the system impedance, resulting in voltage waveforms that exhibit similar sequences at various points along the system impedance. The degree of electrical coupling between two measurement points can be assessed by analyzing the similarity of voltage variation waveforms. Common quantitative measures for this purpose include the Euclidean distance, dynamic time warping, and Pearson correlation coefficient. Notably, while Euclidean distance and dynamic time warping lack a normalized basis for judgment, necessitating comparative data analysis for assessment, the Pearson correlation coefficient offers a normalized measure.

The Pearson correlation coefficient (PCC), denoted as $R(X,Y)$, represents a statistical measure ( $\in [-1,1]$) quantifying the extent of linear correlation between two sequences, X and Y. The magnitude of PCC signifies the degree of linear correlation, with a larger absolute value indicating a stronger correlation. A negative PCC signifies a negative correlation. The precise computation of PCC is as Eq. (1).

(1) $$R\left(X,Y\right)={\displaystyle \frac{\mathrm{cov}\left(X,Y\right)}{\sigma X\sigma Y}}$$

In Eq. (1), $\mathrm{c}\mathrm{o}\mathrm{v}\left(X,Y\right)$ represents the covariance between one sequence, while $\sigma X$ and $\sigma Y$ denote the standard deviation of sequences $X$ and $Y$, respectively. This article utilizes the PCC to assess the relationship between users and stations. Initially, a threshold δ is established. If the calculated correlation, $R(X,Y)$, surpasses δ, it signifies a robust correlation between the two sequences, even when there is a substantial disparity. In such instances, the topological connection between the user and the Substation is deemed accurate. Conversely, if $RR(X,Y)<\delta$, it indicates a weak correlation between the two sequences, implying an error in the topological connection between the user and the Substation, necessitating on-site verification.

The TSS algorithm serves two distinct applications: 1. The TSS algorithm can identify instances when model parameters or the model itself undergo changes. 2. TSS can generate a higher-level time series representation, applicable for indexing, clustering, classification, inconsistency discovery, and anomaly detection within time series data. These two application scenarios impose specific requirements on the TSS algorithm. In Scenario 1, the TSS algorithm must possess the capability to identify the time instances when changes occur in the system model. In Scenario 2, the TSS algorithm divides time series data into non-overlapping subsequences. In the context of this study, the voltage time series of users is segmented to enhance the precision and speed of topology verification. Subsequently, these subsequences are extracted to provide a more robust representation of users’ power consumption characteristics. Building on this foundation, the article delves into the correlation between the substation and the voltage time series of users.

HMM

The HMM stands as a widely employed probabilistic model for the analysis of sequential data. In this study, the HMM model is harnessed to address the issue of PLTI. The HMM model effectively captures and infers the topological states within power systems by encapsulating the statistical relationship between hidden states and observable sequences. This approach contributes to an improved understanding and analysis of the topological characteristics and variations among power network nodes. To align with the research objectives, a constraint is introduced in the form of the minimum continuous state length associated with change points. This constraint serves to regulate state transitions within the HMM model, ensuring its alignment with actual power systems. Subsequent sections of this article provide a comprehensive elucidation of the construction and optimization process of the constrained HMM, along with its practical application in the realm of PLTI.

HMMs can be categorized into two types: first-order HMMs and higher-order HMMs. HMM represents a dual random process where the transition from one state to another follows a random pattern, constituting an implicit finite-state Markov chain. Concurrently, the observations within a state are also subject to randomness, establishing a statistical correlation between the state and the observations. Figure 4 illustrates the underlying principle of HMM. The mathematical formulation of HMM is articulated through Eqs. (2) and (3).

(2) $${\mathrm{q}}_{\mathrm{t}}\in \mathrm{S}=\left\{{\mathrm{s}}_1,{\mathrm{s}}_2\dots {\mathrm{s}}_{\mathrm{N}}\right\}$$

(3) $${\mathrm{o}}_{\mathrm{t}}\in \mathrm{V}=\left\{{\mathrm{v}}_1,{\mathrm{v}}_2,\dots ,{\mathrm{v}}_{\mathrm{M}}\right\}$$

In Eq. (2), S signifies the hidden state set, and N denotes the total number of states. The state of the hidden state chain at time $\mathrm{t}$ is represented ${\mathrm{q}}_{\mathrm{t}}\in \mathrm{S}$.

A general HMM does not impose any restrictions on the transitions between hidden states, allowing for unrestricted transitions between states. This is referred to as an unconstrained HMM. However, real-world applications often operate within specific industrial contexts. Consequently, an HMM needs to undergo training to align with diverse user requirements. In other words, constraints are typically applied to the HMM or the decoding of hidden state sequences in practical scenarios. Such an HMM is known as a constrained HMM.

This study introduces an HMM that incorporates a constraint related to the minimum continuous length of states, thereby regulating state transitions. Consequently, the constrained HMM is represented as a new five-tuple denoted as ${\mathrm{\lambda }}^{\mathrm{\prime }}=\left({\mathrm{S}}^{\mathrm{\prime }},{\mathrm{V}}^{\mathrm{\prime }},{\mathrm{A}}^{\mathrm{\prime }},{\mathrm{B}}^{\mathrm{\prime }},{\pi }^{\mathrm{\prime }}\right)$. The minimum continuous length of a state, denoted as $\mathrm{h}$, adheres to the constraint $1\le \mathrm{h}\le \mathrm{T}$.

The hidden state set, denoted as ${\mathrm{S}}^{\mathrm{\prime }}$, is expanded to accommodate ${\mathrm{N}}^{\ast }\mathrm{h}$ hidden states. In a general HMM, the hidden state set is represented as s $=\left\{{\mathrm{s}}_1,{\mathrm{s}}_2,\dots ,{\mathrm{s}}_{\mathrm{N}}\right\}$, and it is expanded by a factor of H. Specifically, ${\mathrm{s}}_1$ is extended to $\left\{{\mathrm{s}}_{11},{\mathrm{s}}_{12},\dots ,{\mathrm{s}}_{1\mathrm{h}}\right\}$; ${\mathrm{S}}_2$ extends to $\left\{{\mathrm{s}}_{21},{\mathrm{s}}_{22},\dots ,{\mathrm{s}}_{2\mathrm{h}}\right\}$; ${\mathrm{S}}_{\mathrm{N}}$ extends to $\left\{{\mathrm{s}}_{\mathrm{N}1},{\mathrm{s}}_{\mathrm{N}2},\dots ,{\mathrm{s}}_{\mathrm{N}\mathrm{h}}\right\}$. In the output probability matrix and during the analysis of the state chain, $\left\{{\mathrm{s}}_{11},{\mathrm{s}}_{12},\dots ,{\mathrm{s}}_{1\mathrm{h}}\right\}$ is considered equivalent to ${\mathrm{s}}_1$. By extension, the state of the hidden state chain within the expanded set ${\mathrm{S}}^{\prime }=\left\{{\mathrm{s}}_{11},{\mathrm{s}}_{12},\dots ,{\mathrm{s}}_{1\mathrm{h}},\dots ,{\mathrm{s}}_{\mathrm{N}\mathrm{h}}\right\}$ is represented as ${\mathrm{q}}_{\mathrm{t}}$, where ${\mathrm{q}}_{\mathrm{t}}\in {\mathrm{S}}^{\mathrm{\prime }}$. Figure 5 exhibits the construction of this extended hidden state set.

The observation value set, denoted as ${\mathrm{V}}^{\mathrm{\prime }}$, encompasses $\mathrm{M}$ possible observations corresponding to each hidden state, resulting in a total of $\mathrm{M}$ observations. ${\mathrm{V}}^{\mathrm{\prime }}$ is equivalent to the standard observation value set $\mathrm{V}=\left\{{\mathrm{v}}_1,{\mathrm{v}}_2,\dots ,{\mathrm{v}}_{\mathrm{M}}\right\}$. Assuming the observation value at time t is ${\mathrm{o}}_{\mathrm{t}}$, then it follows that ${\mathrm{o}}_{\mathrm{t}}\in {\mathrm{V}}^{\mathrm{\prime }}$. In essence, the observation value set remains consistent with that of a general HMM.

Vector ${\pi }^{\mathrm{\prime }}$, representing the initial state probabilities, is defined as follows: $\pi =\left\{{\pi }_1,\dots ,{\pi }_{1\mathrm{h}},\dots ,{\pi }_{\mathrm{N}\mathrm{h}}\right\}$. In this notation, ${\pi }_{\mathrm{i}\mathrm{m}}$ signifies $\mathrm{P}\left({\mathrm{q}}_1={\mathrm{s}}_{\mathrm{i}\mathrm{m}}\right)$, where $1\le \mathrm{i}\le \mathrm{N}$. It quantifies the likelihood of the initial state of the sequence being ${\mathrm{s}}_{\mathrm{i}\mathrm{m}}$.

In the hidden state transition probability matrix ${\mathrm{A}}^{\mathrm{\prime }}$, denoted as ${\mathrm{A}}^{\mathrm{\prime }}={\left({\mathrm{a}}_{\mathrm{i}\mathrm{m},\mathrm{j}\mathrm{n}}\right)}_{\mathrm{N}\mathrm{h}\times \mathrm{N}\mathrm{h}}$, the elements ${\mathrm{a}}_{\mathrm{i}\mathrm{m},\mathrm{j}\mathrm{n}}$, signify the probability of transition from state ${\mathrm{s}}_{\mathrm{i}\mathrm{m}}$ to ${\mathrm{s}}_{\mathrm{j}\mathrm{n}}$, expressed as $\mathrm{P}\left({\mathrm{q}}_{\mathrm{t}+1}={\mathrm{s}}_{\mathrm{j}\mathrm{n}}\mid {\mathrm{q}}_{\mathrm{t}}={\mathrm{s}}_{\mathrm{i}\mathrm{m}}\right)$, where $1\le \mathrm{i},\mathrm{j}\le \mathrm{N}$, and $1\le \mathrm{m},\mathrm{n}\le \mathrm{h}$. It is important to note that the constraints imposed on state transitions necessitate that, distinguishing it from the general HMM. To illustrate this distinction, consider the case of having two states and h = 3. In this scenario, the state transition matrix is represented as shown in Eq. (4).

(4) $$A^{\mathrm{\prime }}=\left[\begin{array}{cccccc}0& a_{11,12}& 0& 0& 0& 0\\ 0& 0& a_{12,13}& 0& 0& 0\\ 0& 0& a_{13,13}& a_{13,21}& 0& 0\\ 0& 0& 0& 0& a_{21,22}& 0\\ 0& 0& 0& 0& 0& a_{22,23}\\ a_{23,11}& 0& 0& 0& 0& a_{23,23}\end{array}\right]$$

Figure 6 outlines the general steps involved in constructing a constrained HMM. Subsequently, building upon the principles of discrete HMM theory, a time series model based on the constrained HMM is developed. The initial step in this process involves discretizing the time series into ${\mathrm{o}}_{\mathrm{t}}$, tailored to the specific requirements of the application context.

In the context of PLTI, this article utilizes the HMM algorithm to tackle the recognition problem. The HMM model, which captures the statistical relationship between hidden states and observable sequences, facilitates the modeling and inference of topological states within power systems. To better align the HMM model with the characteristics of real power systems, a constraint is introduced based on the minimum continuous state length associated with change points. This constraint serves to expand the number of hidden states in the state set and imposes restrictions on the state transition matrix. These adjustments aid in interpreting node connectivity in the power network, ultimately enhancing the accuracy and reliability of topology recognition.

The application of the HMM to data analysis and topological inference in PLTI enables intelligent management and operational support for low-voltage distribution substation areas. The HMM model serves as a valuable tool for gaining a deeper understanding and analysis of the topological characteristics and variations among nodes within the power network. When integrated with other techniques, the HMM model enhances the accuracy of topology recognition, offering critical support for system operation and management.

This section lays the theoretical foundation and provides methodological support for applying the HMM model in PLTI. The following section presents a specific application scenario, emphasizing the composition and functionality of the LVDN substation identification system. Utilizing the HMM model for data analysis and topology recognition within this system enables intelligent management and operational support for low-voltage distribution substations.

Composition and function of the LVDN-oriented substation topology identification system

The LVDN substation identification system is a comprehensive system that encompasses multiple electrical components and branches, all meticulously designed to accurately determine the topology of LVDN substations. These components operate collaboratively to ensure the seamless functioning of the distribution substation.

At the core of this system lies the power source, a pivotal component responsible for providing energy. It generates electricity and distributes it to various electrical devices. The power source can take the form of either a conventional generator or a contemporary integrated renewable energy device.

The bus assumes a crucial role within the system as the primary conductor, interconnecting various electrical devices. Its principal function is to transmit electrical energy from the power source to the substation’s components while regulating the voltage level to meet the requirements of different devices. The bus is connected to components such as generators, transformers, and switches through branches, forming the primary pathway for electrical energy transmission.

Transformers hold a central position in the system, primarily responsible for voltage level adjustment. They facilitate the conversion of high voltage to low voltage or vice versa, ensuring compatibility with the operational needs of diverse devices. Interconnected with the bus and feeder lines via branches, transformers efficiently regulate the transmission and distribution of electrical energy.

Switches are fundamental devices essential for controlling the flow of electric current. Their capacity to either open or close circuits is pivotal in the distribution and regulation of electricity. Within the context of the LVDN substation identification system, switches assume a central role in directing electrical energy to various branches and feeder lines. This functionality is critical for effectively managing and controlling the flow of electricity throughout the system.

Feeder lines play a crucial role in the transmission of electrical energy from the transformer to end-users within the substation. Their primary responsibility is to distribute electricity to a variety of electrical devices and users, guaranteeing a continuous and uninterrupted power supply. These feeder lines achieve this by establishing connections between transformers and switches through branches, thus forming the vital conduit for the transmission of electrical energy.

Branches serve as vital pathways, establishing interconnections among various electrical components. They facilitate the flow of electrical energy, originating from the power source, through the bus, transformers, switches, and other elements, before finally reaching the end-users. The design and operation of branches play a pivotal role in determining the efficiency and reliability of the substation identification system. Well-designed branches are instrumental in ensuring the effective transmission and stable provision of electrical energy.

Experimental design

(1) Data source

This section conducts a case analysis using user data obtained from a substation under the jurisdiction of X city, collected by the state grid Power consumption information acquisition system. The input data consists of three days’ worth of single-phase user voltage measurements, obtained from the historical records of the substation, with a data collection rate of 100%. The substation serves 125 single-phase users, distributed across 16 secondary access meter boxes operating under three-phase configurations, with no three-phase users present. Each user’s dataset comprises 190 voltage measurements. The initial phase of the experiment focuses on identifying the user phase and access meter box within the designated low-voltage platform area. Subsequently, the method proposed in this article’s analysis is compared to other methods in terms of user phase identification accuracy.

(2) Selection of experimental content and evaluation index

In the experiment, the investigation begins with user phase and meter box identification, followed by a comparative analysis of the method against existing approaches to assess user phase identification errors. Subsequently, in line with the specific requirements of power system topology identification tasks and the experimental design, the research examines the influence of adjusting the discretization granularity on user phase identification accuracy. The discretization granularity is varied within the range of 5% to 18%. Next, the algorithm’s resistance to noise is evaluated. Various noise levels, characterized by standard deviations of 0.01 and 0.1, are introduced to simulate real-world power data noise. A performance comparison is conducted between the proposed improved HMM algorithm and previously existing algorithms, including the classical HMM algorithm. Finally, the experiment records the execution times of different algorithms to gauge their efficiency. Additionally, the assessment covers energy utilization efficiency and load balancing to understand their impact on the power system.

Error analysis

Figure 7 illustrates the assessment of user phase identification errors using the HMM algorithm under different discretization granularities. In Fig. 7, the optimized HMM algorithm demonstrates strong convergence on the test data. As the number of iterations increases from 10 to 100, the model error consistently decreases. Notably, the learning speed of the model is influenced by the length of the sample data (time series length). When the time series length is short, the reduction in model error occurs at a slower pace, leading to a more substantial gap between the learned weight matrix and the actual weight matrix. Conversely, with a longer time series length, the model error decreases more rapidly, reaching an optimal solution in as few as 50 iterations. Upon comparing the algorithm introduced in this article with the recent study conducted by Li et al. (2023), it is evident that both algorithms exhibit a comparable number of iterations. This similarity in iteration counts indicates that the algorithm presented in this article efficiently attains an optimal solution, aligning with the observations made in the study by Li et al. (2023).

Verification and comparison of algorithm anti-noise performance

Figure 8 presents a comparative evaluation between the standard HMM algorithm and the proposed optimized HMM algorithm, denoted as “HMM (1),” at noise standard deviations of 0.01 and 0.1. HMM (1) in Fig. 8 is the optimized HMM algorithm.

Figure 8 illustrates the considerable superiority of the enhanced HMM algorithm, especially when dealing with a substantial volume of sample data. In contrast to the conventional HMM algorithm, the improved variant excels in scenarios with a higher number of samples, showcasing enhanced learning capabilities and reduced errors. These findings suggest that the enhanced HMM algorithm is well-suited for achieving more precise topology identification of power lines in real-world applications.

Algorithm comparison

Table 1 demonstrates that the enhanced HMM method, when compared to full-day data analysis, introduces only a modest increase in computational time while significantly elevating the accuracy of the discrimination process. Although the sliding time window analysis method exhibits the highest precision, its computational time is 50 times that of the improved HMM method, which could become prohibitively time-consuming in the context of a large-scale power grid. Nevertheless, the enhanced HMM method exhibits substantial potential for practical applications within this domain. To address the issue of threshold selection while maintaining high precision, a dual-threshold verification strategy can be employed, particularly well-suited for user data with precision levels ranging from 0.90 to 0.95. This approach is designed to mitigate the risk of misclassifications while efficiently managing computational resources.

The algorithm performance evaluation in this article includes a comparative analysis of energy efficiency and load balance. Table 2 presents the energy utilization efficiency and load balancing degree of the three algorithms.

Table 2 provides insights into different algorithms’ energy utilization efficiency and load balancing performance. The results show that the full-day data analysis algorithm exhibits an energy utilization efficiency of 0.75, slightly outperformed by the sliding time window analysis algorithm, which achieves an efficiency of 0.82. In contrast, the enhanced HMM algorithm, developed based on the power grid topology model presented in this study, demonstrates superior energy utilization efficiency, with a value of 0.89. These findings indicate that the improved HMM algorithm is more adept at optimizing energy resource utilization within the power system. In terms of load balancing, the full-day data analysis algorithm yields a load balance index of 0.62, while the sliding time window analysis algorithm achieves a higher index of 0.78. Notably, the enhanced HMM algorithm attains the highest load balance index at 0.85. This underscores the enhanced HMM algorithm’s capacity to excel in load balancing within the power system, ensuring a more equitable distribution of loads among different nodes. As a result, the improved HMM algorithm contributes to enhanced stability and reliability in the power system.