The high-voltage power cable performance indicators serve as quantitative representations of cable performance, guiding monitoring, analysis, and control efforts. In this study, based on field research of a local cable, five indicators including body temperature, load current, maximum-to-minimum ratio of single-phase grounding current, ambient temperature, and ambient humidity, are selected to form the evaluation factor set U. The cable body temperature refers to the temperature of the cable core, while the ambient temperature and humidity refer to those within the cable tunnel. These indicators are crucial for assessing and ensuring the operational efficiency and safety of high-voltage power cables. The content shown in Figure 2 analyses and evaluates the status of the cable (Tan et al., 2017; Hu et al., 2017; Shao and Bowler, 2019; Ding et al., 2022; Lee et al., 2023).

The condition of the cable should be classified according to the condition of the high-voltage cable condition testing technology specification to achieve its specific performance. Accordingly, this paper classifies three conditions of the cable: normal, attention, and defective. The normal condition refers to when the cable tunnel operates normally. The attention condition indicates that it requires strengthened monitoring. The defective condition signifies that a defect is likely to occur with high probability, and thus requires close monitoring. Therefore, the evaluation set is composed, as shown in Equation 6: V = v 1 v 2 v 3 T = Normal condition   Attention condition   Defective condition T (6)

According to fuzzy judgment, the weight distribution of each factor significantly influences the judgment result; Therefore, determining a reasonable weight set becomes one of the key points and difficulties in fuzzy judgment.

We conduct empirical studies by utilizing expert opinions to assess the importance of each factor within its corresponding set, the importance values are rated on a scale from 1 to 9, and form a judgment matrix. Hierarchical analysis is then employed for pairwise comparisons of factors with different levels, ensuring test consistency. The weighting of factors in the preceding layer is reflected by the largest eigenvalue associated with the corresponding eigenvectors, following the methodologies discussed by Azadeh and Abdolhossein Zadeh (2016), Fang et al. (2018), and Sokolović et al. (2021).

The performance state of a high-voltage cable can be represented by a set of state characteristic parameters such as x 1 , x 2 , ⋯ , x n , which can be written as x i t . To quantitatively assess the change in cable performance from the normal state to a fault state, a measure value of deterioration is used which is denoted as g i . This measure value represents the degree of deviation of the equipment from its normal state and takes values in [0, 1]. In the context of positive deterioration, the state quantity is characterized by an increment of its value. Specifically, a degree of deterioration of 1 means that the ith performance state of the cable is poor, whereas a degree of 0 indicates that the ith performance state of the cable is in satisfactory condition (Hua et al., 2013; Seguchi et al., 2015). Conversely, in the case of negative deterioration, the state quantity is represented by a decrement in its value, which reflects an inverse relationship with the degree of degradation.

The condition parameters used to assess the state of the cable include various indicators. The cable operating parameters are shown in Figure 2, where the first four indicators typically indicate positive degradation—increasing values correlate with degradation. Conversely, ambient humidity is a negative degradation indicator, lower values contribute more to faults. g i = 1 − x m − x i x m   x i ≤ x m 1   x i > x m (14) where x m is the threshold value of the indicator state parameter; x i is the actual measured value of the indicator.

Considering the significant impact of air humidity on fire occurrence and the technical regulations for cable detection, the degradation of indicators such as conductor temperature, load current, ratios of maximum value and minimum value of single-phase ground current, ambient temperature, and humidity are calculated using Equations 15–19: they are borrowed from Equation 14. Some parameters in the following formulas can be obtained by querying relevant standards. g i = 1 − 90 − x i 90   x i ≤ 90 1   x i > 90 (15) where x i is the actual measured value of conductor temperature g i = 1 − x m − x i x m   x i ≤ x m 1   x i > x m (16) where x m is the rated current carrying capacity of the cable line and x i is the actual measured value of the indicator. g i = k * 1 − 3 − x i 3   x i ≤ 3 1 * k   x i > 3 (17) where x i is the ratio of the maximum value and minimum value of the measured single-phase grounding current. k is a parameter whose value is determined as follows: If x i ≤ 3 , about the A, B, and C phases, if the maximum value of single-phase current measurement belongs to a phase, its parameter k is 1; the k value of the phase to which the intermediate value belongs is 0.8; the parameter k of the phase to which the minimum value belongs is 0.6. If x i > 3 , the corresponding three values of k are 1, 0.7, and 0.5. g i = 1 − 35 − x i 35   x i ≤ 35 1   x i > 35 (18) where, x i is the measured value of ambient temperature.

The occurrence of fire is closely related to air humidity. Fire is less likely to occur when air humidity is more than 60%. In the range of 50%–60% humidity, fire can burn slowly but does not spread easily. With 40%–50% humidity, combustion can produce smoke but does not spread extensively. When humidity drops to 30%–40%, fire ignites more readily and can spread further. Humidity below 25% will significantly increase the risk of fire. The degree of air humidity contribution to cable failure can be expressed as: g i = x i 100 %   x i > 25 % 0   x i ≤ 25 % (19) where x i is the measured value of ambient humidity.

The fuzzy evaluation matrix represents the relationship between the factor set and the evaluation set. It utilizes cable indicators to gauge the degree of deterioration, which determines the degree of different states within the state space. The triangular distribution function categorizes objective entities into large, medium, and small groups. Evaluating sets across normal, attention-worthy, and defective classifications aligns perfectly with the triangular distribution function’s description, depicted in Figure 3. Therefore, we employ the indicator’s deterioration degree combined with the triangular distribution function to determine the membership function’s degree.

Based on the parameter ranges of each evaluation index of the cable, the degree of deterioration for each system factor can be calculated by Equations 20–22. By calculation, we can obtain these degrees of membership relative to the evaluation set, thereby we can construct R. r v 1 g i = 1 g i < 0.3 0.6 − g i 0.3 0.3 ≤ g i ≤ 0 0 g i > 0.6 . 6 (20) r v 2 g i = 0   g i < 0.3 g i − 0.3 0.3   0.3 < g i ≤ 0.6 0.9 − g i 0.3   0.6 ≤ g i ≤ 0.9 0   g i > 0.9 (21) r v 3 g i = 0   g i < 0.6 g i − 0.6 0.3   0.6 ≤ g i ≤ 0.9 1   g i > 0.9 (22)

In fuzzy comprehensive evaluation, the “o” operator is applied in various ways, with the principle of maximum affiliation being the most commonly used method in practice. However, in certain cases, using only this method can lead to significant information loss and even produce unreasonable evaluation outcomes. In this paper, we propose a method that considers the weights of each evaluation factor of the cable system. It utilizes the fuzzy relationship matrix, which is formed based on the degree of affiliation of each factor. The approach involves using a weighted average as the fuzzy comprehensive evaluation operator which is expressed as follows: b j = ∑ i = 1 n w i ⋅ r i j j = 1 , 2 , ⋯ , m (23)

The model takes into account the effects of all factors and retains all the information from the single-factor assessment, which makes it well-suited to engineering assessment.

This paper analyses a 220 kV double-circuit cable system in a city as an example. The cable length is 9.422 km, and the type of cable is YJLW03-220-1*1000. Both cable and its accessories were produced by one company. The double-circuit line was put into operation on 30 June 2008, it was equipped with 16 sets of intermediate connectors, one set of GIS terminals for the cable, and one set of outdoor terminals. Before the cable failure occurred in Joint No. 3, the cable was working normally. On 19 December 2019, the cable operation and inspection department conducted routine tests on this joint, including temperature measurement, circulating current measurement, partial discharge detection, etc. All the test results were normal. Table 2 shows the operating and environmental parameter measurements of Joint No. 3.

The analytical hierarchy process method was used to calculate the weight of each factor. Using the fuzzy comprehensive evaluation method, the corresponding deterioration degree was calculated based on the measured value, and the parameters and calculation results are shown in Table 3.

A comprehensive evaluation is conducted based on Equations 5, 23, the results of the comprehensive evaluation of the three phases A, B, and C were calculated as Equations 24–26: B A = W ∘ R A = 0.4323 0.5636 0.0385 (24) B B = W ∘ R B = 0.3621 0.3963 0.2374 (25) B C = W ∘ R C = 0.3621 0.1373 0.4964 (26)

According to the principle of maximum affiliation, the A and B phases should be categorized under the state of attention, while the C phase is in the state of defective. Theoretically, if our proposed method was applied it can suggest that monitoring efforts should be intensified for the A and B phases, whereas the C phase should be further inspection and investigation into the cause of its state. However, the test data on 19 December 2019 indicated that the cable was in normal condition; therefore, no further inspection has been done in accordance with the technical specifications. At 23:46 on 11 July 2020, a fault occurred in Joint No. 3 of the C phase of the 220 kV double-circuit cables, which led to severe rupture and burning of the joint, as shown in Figure 4.

The cable fault assessment method proposed in this paper demonstrates its ability to provide a very early warning, which is almost 6 months before the fault occurs. The assessment results can serve as valuable references for inspection and maintenance personnel.