On-Line Insulation Monitoring Method of Substation Power Cable Based on Distributed Current Principal Component Analysis

1. Introduction

The power cable in a substation transmits electrical energy throughout the entire system. Ensuring its proper insulation is crucial for maintaining stable operation of the substation [1]. On the one hand, as the working years increase, the power cables of the substation power system are easily deteriorated due to the harsh working environment and voltage stress. This will hinder the normal transmission of electric energy and even cause fires in serious cases [2,3,4]. Therefore, it is very important to carry out research on power cable insulation monitoring methods suitable for substations [5,6].

Since off-line cable insulation assessments consume significant financial and human resources, and certain critical loads in the substation power supply system cannot be powered off, on-line insulation monitoring is more suitable [7,8]. To enable real-time monitoring of cable insulation status, many researchers have proposed various methods, including partial discharge (PD) signal measurement, AC superposition, DC superposition, dielectric parameter measurement, and leakage current measurement [9]. These methods offer effective ways to assess insulation conditions without interrupting power supply to critical systems.

Among these methods, the on-line partial discharge (PD) signal method diagnoses the insulation status of cables by measuring high-frequency signals generated during partial discharge events in the cable insulation. However, these signals often overlap with external noise, requiring advanced signal processing techniques. Additionally, there is a lack of standardized and scientific evaluation criteria [10].

The AC superposition method involves applying an AC voltage of a specific frequency to the cable shielding layer and detecting a characteristic current signal at 1 Hz, which indicates the aging of the cable. This method was first introduced by Japanese scientist Takao Kumazawa [11]. However, in operational substations, it is challenging to measure such a small signal due to strong interference.

The DC superposition method injects a low-voltage source at the neutral point and uses a high-sensitivity ammeter to measure the leakage current or insulation resistance through the cable insulation layer. This method is only suitable for systems with ungrounded neutral points on the load side. Additionally, it measures only the overall insulation resistance of the line while neglecting distributed capacitance information, which hinders a comprehensive assessment of the cable’s insulation condition [12].

The insulation dielectric loss method involves applying voltage to the cable and measuring the current flowing through the insulation layer via a voltage transformer and a current transformer [13,14]. The insulation loss factor (tan δ) is then calculated to determine the cable’s insulation quality. However, this method is not applicable to three-phase cables laid in substation cable trenches, where high voltages and strong interferences can significantly affect detection. Moreover, the normal dielectric loss factor of cable insulation is typically very small, which makes it prone to interference in the on-line monitoring system [15].

In recent years, the leakage current measurement method has gained attention due to its strong resistance to electromagnetic interference and its ability to provide quantitative assessments [16,17]. However, in substation power supply systems, challenges such as neutral line shunting on the load side and phase-to-neutral line isolation within power cabinets complicate leakage current measurements. Furthermore, since the leakage current is typically at the milliampere (mA) level, reducing sensor error interference and improving measurement accuracy are critical issues for applying this method to insulation monitoring of substation power cables.

In response to the aforementioned challenges, this paper proposes an on-line leakage current monitoring method for substation power supply systems. The main contributions are as follows:

(1) A method for on-line monitoring of leakage current in substation power supply systems based on distributed current measurement is proposed. The proposed method can solve the issue that the leakage current cannot be directly measured due to the neutral line shunting on the load side and the separation of the phase line and neutral line in the power cabinet.

(2) A mathematical model of the leakage current distribution of power cables in substations is established, and the main factors of leakage current changes in substations are analyzed.

(3) A method for evaluating the deterioration state of power cables in substations based on the principal component analysis method was proposed. This method can reduce false alarms caused by sensor errors when the unbalanced current is large and accurately judge the deterioration of cable insulation.

The rest of this paper is organized as follows. The leakage current monitoring method of substation power cable based on distributed current extraction is introduced in Section 2. The power cable insulation monitoring method and process based on principal component analysis are proposed in Section 3. In Section 4, the proposed method is simulated and verified. In Section 5, the laboratory test is carried out to further prove the applicability of the method. The last part summarizes the contribution of this paper.

3. Power Cable Insulation Monitoring Method Based on Principal Component Analysis

In the process of distributed current extraction, since the synthesized leakage current is only at the mA level, when the single-node measured current is large, the measurement error introduced by the sensor has a serious impact. To address this problem, this paper proposes a distributed current principal component analysis method for substation power cable insulation status monitoring. Through the distributed current extraction method, secondary current information that can reflect the line operation status is obtained [22]. Under the constraint of the short-term invariant characteristics of the leakage current signal, combined with the acquired information, the statistical analysis method can be used to perform an error-free evaluation of the line insulation degradation status and evaluate the measurement error of each node sensor.

The four leakage current collection nodes set are represented as A_j, j = 1, 2, 3, 4. The current data from the four nodes were used to construct a sample matrix X∈R^m*4. Based on the PCA principle, the normalized data matrix A of sample matrix X can be decomposed as follows:

$A = \hat{A} + E = T P^{T} + T_{e} {P_{e}}^{T}$

(6)

where $\hat{A} = T P^{T}$ is a principal subspace model of data matrix A, which contains the main change information of the primary current signal. $E = T_{e} {P_{e}}^{T}$ is a residual subspace model of data matrix A, which contains the measured noise information of the residual space of the sample matrix. T is the principal score matrix, P is the principal load matrix, T_e is the residual score matrix, and P_e is the residual load matrix [23].

The load matrices P and P_e can be obtained by decomposing the singular values of the covariance matrix R of the data matrix A, as shown in the following Equation (7):

$R = A^{T} A / (n - 1) = [P P_{e}] Λ {[P P_{e}]}^{T}$

(7)

where Λ = diag (λ₁, λ₂, λ₃, λ₄), λ₁ ≥ λ₂ ≥ λ₃ ≥ λ₄ is the eigenvalue of the covariance matrix R. [P P_e] is a load vector composed of its corresponding eigenvector. The larger the eigenvalue, the more relevant the variable represented. The variance interpretation for each principal component can be refined as Equation (8):

$V E_{P_{i}} = \frac{Var [P_{i}]}{\sum_{j = 1}^{M} Var [P_{j}]}$

(8)

where Var [P_i] is the variance of the principal component i. By calculating the principal components, the variances are arranged in a decreasing trend, and the first principal component has the highest variance. The number of principal components in the principal component subspace is calculated by the cumulative percent variance (CPV) method. The cumulative sum of the variance contributions of all principal components is greater than the preset value of 85%.

When there is a problem with the insulation state of the cable, the projection of the measured data onto the principal component subspace will deviate to some extent. Similarly, when the measurement error is large, the projection of the measurement data on the residual subspace will also be biased. Hotelling’s T² statistic can be established in the principal component subspace to assess the degree of deviation of the principal components, while the Q statistic can be established in the residual subspace to evaluate the degree of deviation of the residuals in the data. Hotelling’s T² statistic and Q statistic are described as below.

(a) Hotelling’s T² statistic

Hotelling’s T² is the standard sum of squares of the score phasor, which is mainly used to measure the information size of the measurement data projected into the principal element subspace. The specific expression is as follows:

$T^{2} = A^{T} P Λ^{- 1} P^{T} A = \sum_{i = 1}^{P} \frac{t_{i}^{2}}{λ_{i}} \sim \frac{p (n^{2} - 1)}{n (n - p)} F (n, n - p)$

(9)

where p is the number of principal components, F(n,n − p) is the F distribution with n and n − p degrees of freedom and given the confidence level α. The control limits of Hotelling’s T² statistic are shown in Equation (10).

$T_{α}^{2} = \frac{a (n^{2} - 1)}{n (n - a)} F_{α} (α, n - α)$

(10)

Since the T² statistic only contains the principal component score information, it reflects changes in principal component information (information about cable degradation in distributed current data).

(b) Q statistic

The abnormal changes in information that are not projected into the principal component subspace can be judged by calculating the Q statistic in the residual subspace. The specific expression of the Q statistic is as follows.

$Q = (X P_{e} P_{e}^{T}) {(X P_{e} P_{e}^{T})}^{T} = X P_{e} P_{e}^{T} X^{T} \leq Q_{c}$

(11)

where Q_α is the statistical control threshold with a significance level of α, which can be calculated as follows.

$Q_{α} = θ_{1} {[\frac{C_{α} \sqrt{2 θ_{2} h_{0}^{2}}}{θ_{1}} + 1 + \frac{θ_{2} h_{0} (h_{0} - 1)}{θ_{1}^{2}}]}^{\frac{1}{h_{0}}}$

(12)

In the formula, $θ_{i} = \sum_{j = α + 1}^{4} λ_{j}^{i} (i = 1, 2, 3, 4)$ , $h_{0} = 1 - 2 θ_{1} θ_{3} / 3 θ_{2}^{2}$ , C_α is the critical value of the normal distribution at the detection level α.

However, the threshold determination based on Equations (10) and (12) assumes that all score vectors are independent and identically distributed Gaussian variables. In practice, the score vectors obtained after PCA decomposition do not strictly follow a normal distribution. In such cases, kernel density estimation (KDE), a non-parametric method, can be used to calculate the statistical control limits [24].

According to Formulas (9) and (11), the T² statistic and Q statistic of the data matrix are calculated as T² = [T₁, T₂, …, T_m] and Q = [Q₁, Q₂, …, Q_m], respectively. Kernel density estimation can estimate the probability density distribution of a statistic without any assumptions, relying only on the probability density distribution of the statistic.

Taking the T² statistic as an example, T² = [T₁, T₂, …, T_m] is the sampling points of independent and identically distributed F, and the probability density function of F is f(T). Then the kernel density estimate of f(T) at any point T is Formula (13).

$\hat{f} (T) = \frac{1}{m h} \sum_{i = 1}^{p} N (\frac{T - T_{i}}{h})$

(13)

where N is a Gaussian function as a kernel function, and h is a smooth parameter. Then we can obtain the probability density function of the statistic.

$F (x) = \int_{- \infty}^{x} \hat{f} (x) d x$

(14)

Furthermore, the upper and lower thresholds x₁ and x₂ of the statistic can be obtained by setting the effective levels α and β.

$\{\begin{array}{l} x_{1} = F^{- 1} (1 - α) \\ x_{2} = F^{- 1} (1 - β) \end{array}$

(15)

When the monitored Q statistic exceeds the control limit, the contribution rate Q_i of the current data I_i measured at the i-th node to the statistic Q is calculated using Formula (15).

$Q_{i} = {(M_{i} - {\hat{M}}_{i})}^{2}$

(16)

where M_i is the column vector of the measurement data matrix and ${\hat{M}}_{i}$ is the column vector corresponding to the principal subspace data matrix. By counting the nodes with the largest contribution rate, the sensor node most related to the fault can be located.

The insulation status assessment process of power cables in substation power supply systems based on principal component analysis is shown in Figure 4.

First, install leakage current monitoring sensors at the nodes marked in Figure 3. Collect distributed current information to construct the training set data matrix. Standardize the data matrix to obtain the standardized matrix. Calculate the load matrix and score matrix of the standardized matrix. Then decompose the singular value according to Formula (12) to obtain its eigenvalue and corresponding eigenvector. Select the number of principal components p according to the principle that the cumulative contribution rate is greater than or equal to 85%. At the same time, set the monitoring leakage current threshold T_I according to twice the leakage current when the line is initially operating normally. Then carry out continuous monitoring. Collect distributed current information on-line during the operation period of the power supply system and calculate the composite value. First, determine whether it exceeds the leakage current threshold T_I. If exceeded, calculate the T² statistic and Q statistic according to Formula (13) and Formula (15), respectively. And calculate the control limits of the statistic T² and Q according to the training set data according to the KDE method. Determine the fault type based on the comparison results of the statistic and the control limit. If the T² statistic exceeds the control limit, the cable of this loop is considered to be deteriorated and an alarm is issued. If the Q statistic exceeds the control limit, the measurement error is too large or the sensor is damaged. In addition, the contribution of the Q statistic for each sampling location sensor is calculated to locate the faulty sensor.

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Haobo Yang www.mdpi.com

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On-Line Insulation Monitoring Method of Substation Power Cable Based on Distributed Current Principal Component Analysis

1. Introduction

3. Power Cable Insulation Monitoring Method Based on Principal Component Analysis

Greenberg

1. Introduction

3. Power Cable Insulation Monitoring Method Based on Principal Component Analysis

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