1.

INTRODUCTION

With the widespread application of new energy in the power system, the impact of new energy integration on distribution grid differential protection is becoming increasingly significant. New energy sources such as wind and solar energy exhibit intermittency and variability, which severely affect the current and voltage in the distribution network, posing numerous challenges to differential protection. To address these challenges, it is necessary to choose an appropriate communication method to achieve efficient, accurate, and real-time distribution network differential protection for the integration of new energy sources.

In the context of high levels of new energy source integration, distribution networks differ from transmission networks and cannot rely on cost-effective optical fiber communication [1][2][3]. Reference [4] analyzes the fundamental communication processes in substation communication according to the IEC 61850 standard and proposes a data exchange method using logical points for communication. However, this communication still requires the use of existing wireless methods for transmission and lacks universality. Ethernet Passive Optical Network (EPON) technology has become the mainstream communication method in modern distribution networks due to its advantages of high bandwidth, low cost and easy maintenance. Reference [5] leverages EPON technology for feeder differential protection in distribution networks and achieves synchronization between differential protection devices using IEEE 1588. However, EPON technology’s reliability is limited and cannot meet the reliability requirements of differential protection. 5G communication technology offers advantages such as high bandwidth, low latency, high reliability, and wide connectivity. With an end-to-end latency of less than 10ms and very high reliability and air-interface timing accuracy, it theoretically meets the communication needs of distribution network protection [6]. Numerous researchers have explored the application of 5G technology in distribution networks. Reference [7] proposes a distribution network topology-adaptive differential protection technique based on 5G wireless communication. Leveraging the low latency and high bandwidth of 5G wireless communication, it utilizes the sample point interpolation synchronization method to achieve precise fault localization and isolation. Reference [8] validates the end-to-end latency and jitter of differential protection services in a field test environment based on 5G networking, assessing and analyzing the influencing factors at each node and confirming the feasibility of 5G as a communication solution for differential protection in real-world conditions. Reference [9] analyzes the transmission latency jitter in 5G applications for differential protection schemes and presents a data synchronization method that is independent of time stamp information and fixed delay calculations, capable of eliminating the impact of jitter.

5G demonstrates excellent applicability and reliability in wireless transmission for differential protection. However, the significant integration of high proportions of new energy sources can lead to massive data traffic in distribution network differential protection. Additionally, as a wireless transmission technology, 5G exhibits a degree of openness and ubiquity, necessitating the assurance of its security and reliability. In digital communication, higher modulation orders result in increased spectral efficiency but also lead to higher error rates [10]. In summary, the existing wireless differential protection urgently requires an algorithm to reduce its data transmission volume and enhance data reliability.

Compressed sensing enables the sampling and compression of signals with sparse characteristics at low sampling rates, projecting the original high-dimensional signal directly onto a lower-dimensional observation signal. Subsequently, accurate signal recovery is achieved through reconstruction algorithms, significantly reducing the burden on sampling, transmission, and storage[11]. In the electrical power industry, compressed sensing theory has found excellent applications in areas such as power quality, fault location, and harmonic detection[12][13][14]. In summary, this paper proposes a differential protection algorithm for distribution networks based on dual compressed sensing theory. The aim is to enhance the security of distribution network differential protection and reduce the data volume in communication transmission through the use of dual compressed sensing schemes.

2.

WIRELESS COMMUNICATION-BASED DISTRIBUTION NETWORK DIFFERENTIAL PROTECTION AND ITS SECURITY THREATS

Differential protection in distribution networks is based on Kirchhoff’s current law. It requires transmitting electrical information status variables from both ends to the protective relay at the opposite end. This allows the relay to compare the data from both ends to determine the location of faults and whether protection needs to be activated. One significant challenge in distribution network differential protection is the establishment of communication channels. While optical fiber communication has been well-established for differential protection in transmission networks, it poses a high construction cost when used exclusively in distribution networks. The evolving maturity of wireless communication technology offers a viable solution to the communication transmission issues in distribution network differential protection. As shown in Figure. 1, the typical wireless communication network structure for distribution network differential protection involves protective devices sending current sampling data to Customer Premises Equipment (CPE). The CPE processes the data and transmits it to a base station, which, through the core network, transfers the information to the opposite end. In such a distribution network, differential protection can utilize real-time data from various nodes, including current and voltage, using wireless communication technologies like 4G, 5G, etc., to make protection decisions.

Figure. 1

The topology diagram for wireless communication-based distribution network differential protection

When distribution network differential protection utilizes wireless communication, it requires the transmission of IP protocol packets. At the transport layer, the widely employed UDP (User Datagram Protocol) is suitable for scenarios with large data volumes and high real-time requirements. The UDP packet frame structure is illustrated in Figure. 2 [6].

Figure. 2

UDP packet frame structure

In the context of wireless communication in distribution networks, there are currently two major challenges. First, there is a substantial increase in data volume due to the high penetration of new energy sources, leading to significant costs associated with data traffic and resource utilization at the endpoints, particularly for differential protection applications. Second, there are concerns about security during the transmission process. Wireless communication methods are inherently open and susceptible to external attacks during data transmission. In the case of wireless differential protection in distribution networks, typical network attacks during the transmission process include [15][16]:

Considering the critical nature of differential protection data and its extensive use in distribution networks, compressive sensing technology can enhance security while reducing data transmission volume. It proves to be applicable in wireless differential protection communication.

3.

THE KEY ISSUES OF APPLYING DUAL COMPRESSIVE SENSING THEORY TO DISTRIBUTION GRID DIFFERENTIAL PROTECTION

The process of compressive sensing is illustrated in Figure 3. The non-sparse signal x, after undergoing sparsification processing, yields a sparse signal s. This sparse signal s, after signal observation, results in the compressed measurement signal y. The measurement signal y can be transmitted to the receiving end, where it can be reconstructed into the original signal using reconstruction algorithms. The three key issues in compressive sensing theory are sparse signal representation, observation matrix construction, and signal reconstruction.

Figure. 3

The flow chart of CS

Distribution network differential protection based on dual compressive sensing scheme primarily utilizes two compressive sensing approaches. During the wireless transmission process of distribution network differential protection, the measurement data for these two compressive sensing schemes are mainly transmitted. As shown in Figure. 2, the data transmitted in the dual compressive sensing scheme is primarily represented as illustrated in Figure. 4, comprising the measurement signals of the two compressive sensing approaches combined.

Figure. 4

Transmitted Data in Dual CS Theory

3.1

Two CS Schemes Applied in Distribution Network Differential Protection

3.1.1

Scheme 1: DCT-Circulant Matrix-OMP

In compressive sensing, a sparse signal means that only a very small number of elements in the signal are non-zero. For current data in differential protection, the Discrete Cosine Transform (DCT) can be used to transform the current signal into a sparse signal. In this context, the DCT transformation matrix can be considered as a sparse matrix. DCT transformation can be viewed as a discrete Fourier transform with the restriction that the input signal must be a real even function. As shown in Equation (1), the basis functions of DCT have good representation capabilities in the low-frequency region, which results in the current signal having good sparsity properties after undergoing the DCT transformation.

In the equation, k represents the index of the basis function, and its values range from 0 to N-1.

The choice of the observation matrix is crucial for the performance of signal reconstruction. In Scheme 1, a circulant matrix is used as the observation matrix. A circulant matrix is a special form of a Toeplitz matrix, where its elements are arranged cyclically around the matrix, as shown in Equation (2). Using a circulant matrix as the observation matrix provides shift-invariance, which means that the characteristics of the signal won’t change when the signal is shifted in time or space during signal processing. Additionally, it allows for more uniform sampling of the signal, leading to more accurate signal reconstruction.

Compressive sensing reconstruction algorithms can be categorized into four types: greedy iterative algorithms, convex optimization algorithms, reconstruction algorithms based on Bayesian frameworks, and other algorithms. In Scheme 1, the orthogonal matching pursuit (OMP) method is employed for decrypting differential protection data.

3.1.2

Scheme 1: DCT-QR-OMP

In Scheme 2, the sparse matrix and reconstruction method are the same as in Scheme 1. The observation matrix is primarily generated through QR decomposition. As shown in Equation 7, QR decomposition represents that an M×N (where M can be equal to N) dimensional matrix A can be decomposed into an M×M orthogonal matrix Q and an M×N non-singular upper triangular matrix R.

The steps for generating the observation matrix in Scheme 2 are primarily as follows:

Generate a random Gaussian matrix A ∈ RM×M.

Perform QR decomposition on A to obtain the orthogonal matrix Q.

Construct an M×N matrix B, where the first M columns consist of the arithmetic square root of M multiplied by the orthogonal matrix Q, and the remaining (N-M) columns are filled with Gaussian random values.

Normalize the matrix B to obtain the observation matrix Φ.

3.2

Confirmation of Compression Ratios for Two CS Schemes.

The compression ratio in compressive sensing is crucial for data transmission. Due to concerns about wireless communication security, the observation matrix and sparse matrix are not transmitted along with the differential protection current data. Therefore, it is necessary to determine the size of the observation matrix in advance. To select an appropriate compression ratio, this paper evaluates the reconstruction performance of compressive sensing algorithms on current signals using Mean Square Error (MSE) and Signal to Noise Ratio (SNR). The calculation methods for these two evaluation metrics are as follows:

Using typical fault current data, simulation calculations were performed for the compression ratios of the two schemes. As shown in Figure. 5, it illustrates the MSE and SNR for both schemes at different compression ratios. Smaller MSE values are preferable, and larger SNR values are better. Taking into account the impact of SNR and MSE on reconstruction performance, a compression ratio of 0.375 can be considered.

Figure. 5

The MSE and SNR of the two CS approaches at different compression ratios

3.3

Distribution Network Differential Protection Based on Dual CS Scheme.

In distribution networks with a high proportion of renewable energy sources, the control characteristics of converters can impact the fault current waveforms, often leading to non-sinusoidal characteristics. This, in turn, results in errors when calculating traditional phase quantities, such as phase vector amplitude and angle, due to the non-fundamental frequency components. The sensitivity of current phasor-based differential protection significantly decreases or may even fail to operate correctly under certain operating conditions. To address this issue, this paper adopts a sample-value differential protection based on time-domain features to mitigate the imbalance error in phase phasor-based differential protection caused by non-fundamental frequency characteristics.

In Equation (9), i_mcs and i_ncs represent the instantaneous values of the currents at the two ends of the line after being processed by the CS algorithm. i_set is the operating threshold for sampled value differential protection and is a positive real number. k is the restraining coefficient.

The basic process of distribution network differential protection based on the dual compressive sensing theory, as proposed in this paper, is outlined in Figure. 6. The fundamental steps are as follows:

• (1) Locally synchronize the acquisition of current data 𝑖_𝑚, Specific synchronization algorithms can include fault-moment self-synchronization [18] or time synchronization based on 5G timing [19], which are not extensively elaborated in this paper.

• (2) Apply compressive sensing Scheme 1 and Scheme 2 to 𝑖_𝑚 for sparse representation and observation to obtain corresponding compressed data 𝑦₁ and 𝑦₂, Combine 𝑦₁ and 𝑦₂ and send them to the remote end.

• (3) Similarly, receive data and sent from the remote end, verify the dimensionality, and then individually reconstruct the compressed data from both ends according to compressive sensing Scheme 1 and Scheme 2 to obtain I₁, I₂, and Perform coefficient verification on and , check whether the values fall within the range of 0.95-1.05. If more than 5 values fall outside this range, it is determined that communication has been subjected to an attack. If communication is normal, proceed to the next step.

• (4) Utilize the data generated from both sides through compressive sensing Scheme 1, I₁ and , for differential protection discrimination.

Figure. 6

The flow of distribution grid differential protection based on dual CS theory

4.

EXPERIMENTAL SIMULATION AND ANALYSIS

To validate the distribution network differential protection under the dual compressive sensing scheme, a distribution network model, as shown in Figure. 7, was constructed using PSCAD/EMTDC. The bus voltage is 10kV, the sampling frequency is set to f=1600 Hz, and there are 32 samples per waveform cycle. The distribution network includes a 121kV infinite bus source G, an inverter-based distributed generation source IIDG1, which is connected to the distribution network through a voltage-boosting transformer, raising 0.69V to 10kV. The line lengths for L1 and L2 are 2km and 1.5km, respectively, with a positive-sequence impedance of z = 0.11 + 0.33jΩ/km. Load 1 has an active power of 2.5MW and a reactive power of 0.3MVAR, while Load 2 has an active power of 4MW and a reactive power of 0.4MVAR.

Figure. 7

Distribution Network Model

4.1

Under normal communication conditions, the operation of distribution network differential protection.

To validate the effectiveness of our approach in differential protection, three-phase short-circuit faults (ABC) and two-phase short-circuit faults (AB) occurred separately at fault locations F1 within the L1 zone and F2 outside the L2 zone. We illustrate the example using phase A data. Figure. 8 represents the differential current and restraining current for both our dual compressive sensing scheme differential protection and traditional differential protection after a fault occurs, while communication remains in good condition. From the Figureure, it can be seen that after the fault occurs, the differential current and restraining current have errors of no more than 0.05, except for specific moments and the fault itself. For clarity, only phase A data is shown in the legends.

Figure. 8

Differential current and restraining current for the approach proposed in this paper and the traditional approach.

From Figure. 9, it can be observed that there is little variation in the differential current between the traditional differential protection and the differential protection approach presented in this paper, with a maximum error of only 0.1. Therefore, according to the criterion (1) in Equation 9, the results of the traditional differential protection and the approach in this paper are essentially the same. As shown in Figureure 16, the differential restraining ratios for the traditional differential protection approach and the differential protection approach in this paper are plotted with a restraining coefficient set to 0.5. From the Figureure, it can be seen that both approaches yield results that are essentially the same according to the criterion (2) in Equation 9.

Figure. 9

Ratio of Differential Current to Restraining Current (AB Phase Fault)

From the above results, it can be observed that the performance of CS differential protection is comparable to that of traditional non-CS differential protection. As shown in Table 1, it presents the operation status of CS differential protection and traditional differential protection under different fault scenarios, along with the operation times for both approaches in different fault conditions. The fault occurrence time is set at 0.5 seconds. From Table 1, it can be seen that the CS sample-value differential protection scheme and the traditional sample-value differential protection scheme exhibit nearly identical operation status and operation times under various fault conditions.

Table 1.

Comparison of CS Differential Protection Scheme and Traditional Differential Protection Scheme Performance

	CS	non-CS
Operation of protection	operating time	Operation of protection	operating time
Internal fault	AB	√	0.50718s	√	0.50718s
ABCG	√	0.506875s	√	0.5065675s
External fault	AB	×		×
ABCG	×		×

4.2

Response of the Approach Proposed in This Paper Under Data Tampering Situation.

In the communication process of distribution network differential protection, it is susceptible to network attacks, as discussed in Chapter 2, including data injection, eavesdropping, and tampering. Data injection can be determined dimensionally. Compressed sensing encrypts the data, effectively protecting it from eavesdropping. This section primarily focuses on data tampering, where the application data in the communication of differential protection is altered. As shown in Figureure 10, a single data point is modified, with the value changed to 0.49, indicating that there has been tampering in the communication of distribution network differential protection. Table 2 presents the altered data, its reconstruction effect, and the corresponding K1 values. For space-saving purposes, only the first 6 data points are shown. From Table 2, it can be observed that in the absence of tampering, the data ratios fall within the range of 0.95-1.05. However, after tampering, the data ratios no longer fall within this range, signaling a network attack during the differential protection communication process.

Figure. 10

Change one value during the transmission process

Table 2.

The value of k after making one modification

	1	2	3	4	5	6
scheme1	-0.1707	-0.16765	-0.16162	-0.15279	-0.14151	-0.12825
scheme2	-0.17294	-0.1697	-0.16342	-0.15455	-0.14366	-0.13118
k1	0.987045	0.987919	0.988961	0.988609	0.984992	0.977692
“After tampering with one data point, scheme 2 reconstructs the data.”	-0.13387	-0.17111	-0.21126	-0.22305	-0.21134	-0.20878
k1’	1.275168	0.979824	0.765019	0.684984	0.669572	0.614278

5.

SUMMARY

For the current security and transmission issues in distribution network wireless differential protection, this paper primarily proposes a theory of distribution network sample-value differential protection based on dual compressive sensing theory. Before transmitting the differential protection data, two compressive sensing schemes are applied to compress the transmission data, reducing the data transmission volume and enhancing data security during transmission. At the receiving end, the transmitted data is reconstructed, and protection determination is performed in comparison with the data compressed at the local end using compressive sensing algorithms. The operation and effectiveness of this approach are similar to traditional differential protection schemes. Additionally, this paper’s approach can identify network attacks during the transmission process, mitigating the impact of data injection, eavesdropping, and tampering on differential protection. Finally, through simulation and analysis, a comparative analysis of the differential and restraining currents, as well as protection operation, is conducted between the proposed differential protection scheme and traditional differential protection schemes. Simulation results indicate that the proposed approach significantly reduces data exchange, enhances security, and can identify the communication status in distribution network wireless differential protection. This is beneficial for the promotion and application of differential protection in distribution networks.