PF and DF may be performed on shielded cable systems to determine insulation degradation to reduce in-service cable failures. These tests are applied as diagnostic testing techniques for field testing of service aged cable systems. For lossless insulation, the cable capacitance (C) per unit length can be defined by the following equation:
k is the dielectric constant of the insulation
is the permittivity (capacitance) of free space (air)
is the diameter over the insulation
is the diameter of the conductor
For cable with conventional insulating materials, the cable conductance (G) per unit length can be defined by the following equation:
The quantity tan d gives the losses in the insulation when subjected to an electric field and is known as DF or the loss angle of insulating material.
The table below provides typical values of dielectric constant k and tan δ.
When a voltage V is applied to the loss-free insulation system (dielectric), the total current IT
drawn by the dielectric is the sum of the capacitive charging current IC
and loss current (resistive) IR
. The angle formed by the current IT
is δ, and the angle formed by the IT
and voltage E is Φ where cos Φ is the PF of the dielectric. The DF (tan δ) test allows an evaluation of an insulation system at operating voltage level and frequency. The tan δ test can also be performed at frequency other than 60 Hz, such as at VLF of 0.1 Hz during proof test conducted at such frequency.
According to IEEE std 400-2001, tests conducted on 1500 miles of XLPE insulated cable have established a figure of merit for XLPE at tan d = 2.2 × 10−3
. If the measured tan d is greater than 2.2 × 10−3
, then the cable insulation is degraded by moisture in the form of water trees (voids in the insulation filled with water), and it is recommended that additional hi-pot tests, such as VLF test be conducted to identify the defects in the cable insulation.
The tan δ test for each conductor with respect to ground should be made. The evaluation should be based upon comparative analysis with previous test results or correlated with test results of similar types of cables.