CN102539964A - Method for judging insulation characteristics of cross linked polyethylene (XLPE) power cables on line - Google Patents

Abstract

The invention relates to a method for judging insulation characteristics of cross linked polyethylene (XLPE) power cables on line, which obtains the temperature and dielectric loss of an insulating layer and relation of insulating thermal resistance by establishing a thermal circuit model of the power cables, further establishes mathematic relation of temperature parameters and dielectric constant of the insulating layer, and judges the insulation damages of current power cables through the dielectric constant of a current insulating layer. According to the dielectric constant of the insulating layer, the method for judging the insulation characteristics of the XLPE power cables on line judges the insulation characteristics of the power cables and learns the insulation damages of power cables, thereby facilitating adoption of corresponding measures and achieving in-advance detection and prevention of accidents.

Description

Judgment method for online insulation characteristics of XLPE power cables

technical field

The invention relates to a judging method, in particular to a method for judging the online insulation characteristics of an XLPE power cable.

Background technique

At present, the transmission and distribution networks of large and medium-sized cities in my country are gradually using high-voltage power cables to replace traditional overhead transmission networks, which is also the premise for the gradual advancement of smart grids and the orderly realization of smart cities. How to safely and stably transmit electric energy on the power cable and extend the service life of the cable becomes extremely important.

The service life of the power cable mainly refers to the service life of the power cable insulation. With the development of electronics, computers, optoelectronics, signal processing and various sensing technologies, the reliability of insulation can be judged at any time and the remaining life of insulation can be predicted, so that potential faults can be found in time.

In recent years, many researchers have proposed some new methods for online live detection of power cable insulation characteristics. These methods are very useful for early detection of insulation defects and aging conditions of power cables, especially XLPE power cables. These methods include:

(1) DC superposition method: Add a low-voltage DC power supply at the neutral point of the grounded voltage transformer to superimpose the DC voltage with the AC voltage of the power cable in operation, and detect the very weak DC current passing through the cable insulation layer. The insulation resistance of the entire cable can be measured to judge whether the cable is good or bad. The DC superposition method is characterized by strong anti-interference ability, but the correlation between the insulation resistance and the remaining life of the cable insulation is not good, and the dispersion is large.

(2) DC component method: By detecting the very weak DC component in the current of the cable core wire and the shielding layer, the degradation diagnosis of the dendification (water tree branch, electric tree branch) insulation defect existing in a certain point or in a certain part of the cable is carried out. The current measured by the DC component method is very weak, and sometimes it is not stable, and a small interference current will cause a large error.

(3) Dielectric loss factor method: Take out the voltage applied to the cable with a voltage transformer or a voltage divider, take out the power frequency current flowing through the insulation with a current transformer, and then detect the above-mentioned signal in the automatic balancing circuit The phase difference can measure the dielectric loss factor of the cable insulation. The dielectric loss factor method is cumbersome to operate and difficult to realize.

(4) Partial discharge method: The partial discharge method uses electromagnetic waves, ultrasonic waves and other signals to detect partial discharges occurring at defects. In theory, it can be detected online, but it is susceptible to background interference and online monitoring is difficult.

(5) Ground wire current method: This method achieves the purpose of monitoring by detecting the increment of the capacitive current passing through the ground wire. This method is simple and easy to implement, and it can be realized by putting a current sensor on the grounding wire, but the grounding wire at the other end of the cable head must be temporarily disconnected during measurement.

(6) Low-frequency superposition method: The low-frequency low superposition method is mainly to superimpose a certain frequency voltage signal on the shielding layer of the cable, amplify the measured degradation signal, and judge the degree of cable degradation according to the strength of the detected degradation signal. This method is simple and easy, and a set of equipment can be used to detect multiple cables, but the disadvantage is that the superimposed electrical signal will have a certain degree of impact on the original system.

Therefore, we urgently need a method for judging the on-line insulation characteristics of XLPE power cables that is simple to operate and can accurately judge the insulation characteristics of power cables.

Contents of the invention

The technical problem to be solved by the present invention is to provide a simple and accurate method for judging the online insulation characteristics of XLPE power cables.

The technical scheme adopted in the present invention is:

A method for judging the on-line insulation characteristics of XLPE power cables, which establishes the thermal circuit model of the power cable to obtain the relationship between the temperature of the insulation layer, the dielectric loss, and the insulation thermal resistance, thereby establishing the mathematical relationship between the temperature parameter and the dielectric constant of the insulation layer , judge the damage of the current power cable insulation by the dielectric constant of the current insulation layer.

The method for judging the online insulation characteristics of XLPE power cables specifically includes the following steps:

The first step is to obtain the skin temperature at a certain point of the power cable and the ambient temperature of the area where the point is located;

The second step is to calculate the current conductor core temperature based on the known current flowing in the current conductor and the ambient temperature

θ _c ＝θ ₀ +[T ₁ +(1+λ ₁ )*T ₂ +(1+λ ₁ +λ ₂ )*(T ₃ +T ₄ )]*W _c +(0.5*T ₁ +T ₂ +T ₃ +T ₄ )*W _d

In the formula:

_θ0 represents the ambient temperature,

θ _c represents the conductor core temperature,

λ ₁ represents the metal shielding loss factor,

λ ₂ represents the armor/reinforcing tape loss factor,

T ₃ represents the thermal resistance of the equivalent outer sheath,

W _c is the conductor power loss per unit length,

T ₂ represents the thermal resistance of the equivalent lining layer,

W _d represents the dielectric loss per unit length,

T ₁ represents the equivalent insulation layer thermal resistance,

T ₄ represents the equivalent external ambient thermal resistance;

The third step is to calculate the temperature difference θ _cm between the conductor core and the insulation layer according to the power cable thermal circuit model:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; cm</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}$

In the formula:

W _c =I ² *R

${\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; tg\&delta;</span>}$

ω=2*π*f

in:

W _c is the conductor power loss per unit length,

T ₁ represents the equivalent insulation layer thermal resistance,

W _d represents the insulation loss, in watts per meter (W/m),

I represents the current flowing in the conductor,

R represents the AC resistance of the cable conductor,

ω denotes the angular frequency of the voltage,

C represents the cable capacitance per unit length,

π stands for pi,

f represents the voltage frequency,

U ₀ is the ground voltage (phase voltage), unit volt (V),

tgδ is the insulation loss factor;

The fourth step is to obtain the change of the dielectric constant ε at this point by calculation, and the calculation formula is:

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; cm</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; tg\&delta;</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 9</span>}}$

In the formula:

θ _cm represents the temperature difference between the conductor core and the insulating layer,

I represents the current flowing in the conductor,

R represents the AC resistance of the cable conductor,

T ₁ represents the equivalent insulation layer thermal resistance,

π stands for pi,

f represents the voltage frequency,

U ₀ is the ground voltage (phase voltage), unit volt (V),

tgδ is the insulation loss factor,

D _i represents the diameter of the insulating layer,

d _c represents the diameter of the conductor;

The fifth step is to compare the dielectric constant ε calculated in the fourth step with the dielectric constant reference table, and obtain the judgment result:

5.1 When the calculated dielectric constant ε is reduced to 50% of the number in the dielectric constant reference table, it indicates that there is an insulation defect, and the power cable must be overhauled;

5.2 When the calculated dielectric constant ε is greater than 50% of the number in the dielectric constant reference table, it indicates that the insulation state is normal.

In the above scheme, in the first step, the skin temperature at a certain point of the power cable and the ambient temperature of the area where the point is located are obtained by point measurement of the fiber grating temperature monitoring system.

The invention obtains the skin temperature at a certain point of the power cable and the ambient temperature in the area where the point is located through the fiber grating temperature monitoring system, and then obtains the relationship between the temperature of the insulating layer, the dielectric loss and the thermal insulation resistance by establishing a thermal circuit model of the power cable . In order to establish the mathematical relationship between the temperature parameter and the dielectric constant of the insulating layer, the current dielectric constant of the insulating layer can be obtained by online detection of the cable temperature, and then reflect the damage of the current cable insulation, and it is convenient to take corresponding measures to achieve early detection , Prevent accidents in advance.

Description of drawings

Figure 1 is a schematic diagram of the structure of an XLPE insulated power cable.

Figure 2 shows the transient thermal circuit model of the power cable.

Figure 3 is the steady-state thermal circuit model of the power cable.

Fig. 4 is a schematic diagram of a fiber grating temperature monitoring system.

In the figure: 1. Conductor; 2. Conductor shielding; 3. Insulation layer; 4. Insulation shielding; 5. Metal shielding; 6. Inner lining; 7. Armored layer; 8. Outer sheath; 9. Temperature probe , 10, connecting optical cable, 11, optical connector, 12, transmitting optical cable.

Detailed ways

Embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

A method for judging the on-line insulation characteristics of XLPE power cables is based on the thermal circuit model of the power cables. The XLPE power cable (XLPE insulated cable) structure is shown in Figure 1. The power cable includes a conductor 1 and an outer sheath 8. Between the conductor 1 and the outer sheath 8, conductors are arranged in sequence from the inside to the outside. Shielding 2, insulating layer 3, insulating shielding 4, metal shielding 5, lining layer 6, and armoring layer 7. The main heating element in the power cable is the conductor. In addition, the various losses of the cable itself are finally dissipated in the form of heat, such as dielectric loss, metal shielding loss, and armor loss. Therefore, the heat source in the thermal circuit model of the power cable should be Including conductor power loss, dielectric loss, metal shielding loss and armor loss. Conductor power loss refers to the loss generated by the conductor, dielectric loss refers to the loss generated by the insulating layer, metal shielding loss refers to the loss generated by the metal shielding layer, armor loss refers to the loss generated by the armor layer), and the losses generated by other layers can be ignored .

The heat emitted by conductor 1 diffuses outwards and must pass through all structures except conductor 1; the heat generated by dielectric loss must pass through several parts such as the metal shielding layer, armor layer, and outer sheath; the heat generated by metal shielding loss must pass through The armor layer and the outer sheath; and the heat generated by the armor loss only passes through the outer sheath.

Considering that the conductor core is made of good heat conductors such as copper or aluminum, the thermal resistance of the conductor core is negligible, and only the heat capacity of the conductor core is considered; the insulating layer 3 can not only prevent the heat from spreading but also Store heat, so the thermal resistance and thermal capacity of the insulating layer 3 should be considered; the thermal resistance of the metal shielding layer 5 and the inner lining layer 6 can also be ignored and only its thermal capacity should be considered; for the outer sheath 8, its thermal resistance and thermal capacity should also be considered. Allow.

Considering the nature of the heat source in the power cable, the heat source in the heat circuit model can be divided into two categories. The external ambient temperature is generally considered constant, which is equivalent to a constant temperature source, so the external environment is equivalent to a constant voltage source in the thermal circuit model; while the conductor core loss, insulation loss, metal shielding loss, and armor loss What is generated is heat, not temperature (according to the knowledge of heat transfer: to heat = temperature difference / thermal resistance), so these kinds of heat sources can be regarded as constant current sources. The lumped parameter method is adopted below (in heat transfer, when the ratio of the heat conduction resistance per unit heat conduction area inside a solid to the heat exchange heat resistance per unit surface area is small, the continuously distributed mass and heat capacity in the object can be regarded as concentrated at one point , the temperature at this point is the lumped temperature) to model it, and its thermal circuit model is shown in Figure 2. Among them, T ₁ , T ₂ , T ₃ , and T ₄ represent the equivalent insulation layer thermal resistance, the equivalent inner lining layer thermal resistance, the equivalent outer sheath thermal resistance, and the equivalent external environment thermal resistance; θ _c represents the conductor line Core temperature, θ _m represents the temperature of the insulating layer, θ _s represents the temperature of the lining layer, θ _e represents the skin temperature, θ ₀ represents the ambient temperature; W _c represents the conductor power loss per unit length, W _d represents the dielectric loss per unit length, λ ₁ Indicates metal shielding loss factor, λ ₂ indicates armoring/strengthening tape loss factor; λ ₁ W _c indicates metal shielding power loss per unit length; λ ₂ W _c indicates armoring power loss per unit length; Q _c , Q _i , Q _s , Q _cp , Q _t and so on represent the heat capacity of the conductor, the heat capacity of the insulating layer, the heat capacity of the inner lining, the heat capacity of the armor, and the heat capacity of the outer sheath; Layer distribution scale factor; D _i represents the diameter of the insulating layer, d _c represents the diameter of the conductor, D _e represents the outer diameter of the cable, D _s represents the inner diameter of the outer sheath, Q ₁ is the equivalent heat capacity between the conductor core and the insulating layer, _Q2 is the equivalent heat capacity between the insulating layer and the inner lining, _Q3 is the equivalent heat capacity between the inner lining and the outer sheath, _{Q4 is} the equivalent heat capacity of the outer sheath, and their expressions are as follows Show:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="Q"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">Q</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="9"\; label="Q\; c\; +"\; filenames="HDA0000123146820000021.png"\; state="\{\{state\}\}">Q</figure-callout></span><figure-callout\; id="9"\; label="Q\; c\; +"\; filenames="HDA0000123146820000021.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="Q\; i\; Q"\; filenames="HDA0000123146820000012.png,HDA0000123146820000013.png"\; state="\{\{state\}\}">Q</figure-callout></span><figure-callout\; id="2"\; label="Q\; i\; Q"\; filenames="HDA0000123146820000012.png,HDA0000123146820000013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}& \\ {}_{}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="Q\; cp\; Q"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">Q</figure-callout></span><figure-callout\; id="3"\; label="Q\; cp\; Q"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; cp</span>}}& \\ {}_{}{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="4"\; label="s\; Q"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">s</figure-callout></span><figure-callout\; id="4"\; label="s\; Q"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">\; </figure-callout>}}& \\ {\mathrm{<span\; class="notranslate">\; </span>}}_{}{\mathrm{<span\; class="notranslate">Q</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; Q</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}\\ \mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}}{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Considering that the insulating layer not only acts as a heat source, but also can store heat, and hinder the propagation and diffusion of heat, the dielectric loss W _d per unit length is divided into two parts, that is, the insulating layer can only hinder the propagation and diffusion of a part of the dielectric loss , whose size is W _d /2; the other half of the dielectric loss passes through the insulating layer and only affects the layers outside the insulating layer. From the analysis of the thermal circuit model, it can be seen that the heat generated by the conductor is transferred to the outer layer to form a heat flow. When the power loss W _c per unit length of the conductor increases, it can cause the conductor core 1, insulating layer 3, inner lining layer 6, outer sheathing layer 8, etc. The rise of the temperature of each layer, if the heat dissipation of the surrounding environment of the cable is blocked or the ventilation is not good, may also cause the rise of the ambient temperature θ ₀ . When the heat flow increases, due to the existence of the heat capacity Q of each layer, the temperature of each layer increases gradually, that is to say, the temperature of each layer cannot change abruptly. When the heat flow does not change and the cable is in a steady state, the heat capacity can be ignored in the calculation of the temperature of each layer, because the heat absorption and heat dissipation of the heat capacity are in a balanced state at this time. The thermal circuit model of the power cable in steady state is shown in Figure 3.

与直流电路中的欧姆定律表达式I＝ΔU/R作对比后可以看出，温差Δt与电压ΔU对应可称为温压，热流Q与电流I对应，因此R_kA便与电阻R对应，称为热截面积A的导热热阻”)，结合图3可得稳态是电力电缆的温度，热流和热阻之间的关系式：From the correspondence between the thermal circuit model and the physical quantities in electromagnetism (see heat transfer: "Formula

Compared with the Ohm’s law expression I=ΔU/R in the DC circuit, it can be seen that the temperature difference Δt corresponds to the voltage ΔU, which can be called temperature and pressure, and the heat flow Q corresponds to the current I, so R _kA corresponds to the resistance R, which is called is the thermal conduction thermal resistance of the thermal cross-sectional area A"), combined with Figure 3, it can be obtained that the steady state is the relationship between the temperature of the power cable, heat flow and thermal resistance:

θ _c ＝θ ₀ +[T ₁ +(1+λ ₁ )*T ₂ +(1+λ ₁ +λ ₂ )*(T ₃ +T ₄ )]*W _c +(0.5*T ₁ +T ₂ +T ₃ +T ₄ )*W _d (2)

At the same time, the temperature expressions of other layers of the power cable can also be obtained:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="4"\; label="T"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; e</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="T"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}\\ {\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

According to the size of the insulation loss and the voltage level of the cable, the type of insulating material used, the size of the conductor capacitance, and the structure of the cable, the calculation formula of the circular conductor capacitance is as follows:

$\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}{\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 9</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In formula (4), ε represents the dielectric constant of the insulating material; Di represents the diameter of the insulating layer excluding the shielding layer, in millimeters (mm); _dc represents the diameter of the conductor, including the shielding layer if there is a shielding layer, in millimeters (mm ); The unit method of potential length cable capacitance c is per meter (F/m). The insulation loss per unit length in each phase is given by:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; tg\&delta;</span>}\\ \mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; f</span>}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In formula (5), W _d is the insulation loss, the unit is watts per meter (W/m), U ₀ is the ground voltage (phase voltage), the unit is volts (V), tgδ is the insulation loss factor, and ω is the angular frequency of the voltage , C represents the potential length cable capacitance.

According to the thermal circuit model, it can be obtained that the temperature difference θ _cm between the conductor core and the insulating layer is not affected by the ambient temperature, but is only affected by the actual current carrying capacity and dielectric loss of the power cable. For a certain fixed carrying capacity, the conductor line The temperature difference θ _cm between the core and the insulating layer is only related to the dielectric loss. Because the operating voltage and structural size of the power cable do not change, the change in the temperature difference θ _cm between the conductor core and the insulating layer can eventually reflect the change in the dielectric constant of the insulating layer, that is, the loss of insulation.

According to the thermal circuit model, the mathematical expression of the temperature difference θ _cm between the conductor core and the insulating layer can be obtained:

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; cm</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

And because the calculation formula of conductor power loss _Wc per unit length is as follows:

W _c =I ² *R (7)

The mathematical relationship between the temperature difference θ _cm between the conductor core and the insulating layer and the dielectric constant ε of the insulating layer can be obtained by combining formula (5), formula (6) and formula (7), as shown in formula (8):

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; cm</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; tg\&delta;</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 9</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

In formula (8),

θ _cm represents the temperature difference between the conductor core and the insulating layer,

I represents the current flowing in the conductor,

R represents the AC resistance of the cable conductor,

T ₁ represents the equivalent insulation layer thermal resistance,

π stands for pi,

f represents the voltage frequency,

U ₀ is the ground voltage (phase voltage), unit volt (V),

tgδ is the insulation loss factor,

D _i represents the diameter of the insulating layer,

d _c represents the conductor diameter.

Through formula (8), it can be obtained that the temperature difference θ _cm between the conductor core and the insulating layer is proportional to the dielectric constant ε of the insulating layer. Considering that in actual operation, the change of the dielectric constant ε of the insulating layer will also cause an equivalent The change of insulation layer thermal resistance T ₁ and insulation loss factor tgδ makes the temperature difference θ _cm between the conductor core and the insulation layer unable to correctly reflect the change of ε through formula (8). But when the current I flowing in the power body takes a fixed value, the temperature difference θ _cm between the conductor core and the insulating layer, the equivalent thermal resistance T ₁ of the insulating layer and the change of the insulation loss factor tgδ are all due to the change of the dielectric constant ε of the insulating layer caused by the change. We assume that when the dielectric constant ε of the insulating layer changes, the equivalent thermal resistance T ₁ of the insulating layer and the insulation loss factor tgδ still take the constant value before the change of the dielectric constant ε of the insulating layer, so that the change of θ _cm is all attributed to the insulation The variation of the dielectric constant ε of the layer. Moreover, at this time, the dielectric constant ε of the insulating layer can be approximated by formula (8). Although this value cannot be regarded as the dielectric constant of the current insulating layer, it can certainly reflect whether the current insulating layer has been damaged.

When the calculated dielectric constant ε is reduced to 50% of the number in the dielectric constant reference table, it indicates that there is an insulation defect, and the power cable must be overhauled; when the calculated dielectric constant ε is greater than that in the dielectric constant reference table When the number is 50%, it indicates that the insulation state is normal.

In view of the above reasons, the present invention provides a method for judging the on-line insulation characteristics of XLPE power cables, which obtains the relationship between the temperature of the insulation layer, the dielectric loss, and the insulation thermal resistance by establishing a thermal circuit model of the power cable, thereby establishing the relationship between temperature parameters and insulation The mathematical relationship of the dielectric constant of the layer can be used to judge the damage of the current power cable insulation through the dielectric constant of the current insulating layer.

The method for judging the online insulation characteristics of the XLPE power cable specifically includes the following steps:

In the first step, the fiber grating temperature monitoring system (see Figure 4) is used to obtain the skin temperature θ _e at a certain point of the power cable and the ambient temperature θ ₀ of the area where the point is located by the temperature probes distributed on the surface of the power cable;

The second step is to calculate the current conductor core temperature based on the known current carrying capacity of the power cable and the ambient temperature

θ _c ＝θ ₀ +[T ₁ +(1+λ ₁ )*T ₂ +(1+λ ₁ +λ ₂ )*(T ₃ +T ₄ )]*W _c +(0.5*T ₁ +T ₂ +T ₃ +T ₄ )*W _d

In the formula:

_θ0 represents the ambient temperature,

θ _c represents the conductor core temperature,

λ ₁ represents the metal shielding loss factor,

λ ₂ represents the armor/reinforcing tape loss factor,

T ₃ represents the thermal resistance of the equivalent outer sheath,

W _c is the conductor power loss per unit length,

T ₂ represents the thermal resistance of the equivalent lining layer,

W _d represents the dielectric loss per unit length,

T ₁ represents the equivalent insulation layer thermal resistance,

T ₄ represents the equivalent external ambient thermal resistance;

The third step is to calculate the temperature difference θ _cm between the conductor core and the insulating layer according to the power cable thermal circuit model;

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; cm</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}$

In the formula:

W _c =I ² *R

${\mathrm{<span\; class="notranslate">\; W</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; tg\&delta;</span>}$

ω=2*π*f

in:

W _c is the conductor power loss per unit length,

T ₁ represents the equivalent insulation layer thermal resistance,

W _d represents the insulation loss, in watts per meter (W/m),

I represents the current flowing in the conductor,

R represents the AC resistance of the cable conductor,

ω denotes the angular frequency of the voltage,

C represents the cable capacitance per unit length,

π stands for pi,

f represents the voltage frequency,

U ₀ is the ground voltage (phase voltage), unit volt (V),

tgδ is the insulation loss factor;

The fourth step is to obtain the change of the dielectric constant ε at this point by calculation, and the calculation formula is:

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; cm</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; tg\&delta;</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 9</span>}}$

In the formula:

θ _cm represents the temperature difference between the conductor core and the insulating layer,

I represents the current flowing in the conductor,

R represents the AC resistance of the cable conductor,

T ₁ represents the equivalent insulation layer thermal resistance,

π stands for pi,

f represents the voltage frequency,

U ₀ is the ground voltage (phase voltage), unit volt (V),

tgδ is the insulation loss factor,

D _i represents the diameter of the insulating layer,

d _c represents the diameter of the conductor;

The fifth step is to compare the dielectric constant ε calculated in the fourth step with the dielectric constant reference table, and obtain the judgment result:

5.1 When the calculated dielectric constant ε is reduced to 50% of the number in the dielectric constant reference table, the power cable must be overhauled;

5.2 When the calculated dielectric constant ε is greater than 50% of the number in the dielectric constant reference table, it indicates that the insulation state is normal.

Fig. 4 shows a schematic diagram of a fiber Bragg grating temperature monitoring system, which is a TGW fiber Bragg grating temperature-sensitive fire detection system product produced by Wuhan Institute of Technology Optical Science and Technology Co., Ltd.

According to the number and position of each fiber grating temperature sensor, the invention divides the whole power cable into small sections to monitor the insulation properties of the insulating layer.

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; cm</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; I</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA0000123146820000011.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; tg\&delta;</span>}}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; ln</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; *</span>{\mathrm{<span\; class="notranslate">\; 10</span>}}^{\mathrm{<span\; class="notranslate">\; 9</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

In the formula

n represents the number of the fiber grating temperature sensor,

ε(n) represents the dielectric constant of the insulating layer at the position of the fiber grating temperature sensor numbered n,

θ _cm (n) represents the temperature difference between the wire core and the insulating layer at the position of the fiber grating temperature sensor numbered n,

I represents the current flowing in the conductor,

R represents the AC resistance of the cable conductor,

T ₁ represents the equivalent insulation layer thermal resistance,

π stands for pi,

f represents the voltage frequency,

U ₀ is the ground voltage (phase voltage), unit volt (V),

tgδ is the insulation loss factor,

D _i represents the diameter of the insulating layer,

d _c represents the conductor diameter.

The invention acquires the skin temperature at a certain point of the power cable and the ambient temperature of the area where the point is located through the fiber grating temperature monitoring system, and then obtains the relationship between the temperature of the insulating layer, the dielectric loss and the thermal insulation resistance by establishing a thermal circuit model of the power cable . Therefore, the mathematical relationship between the temperature parameter and the dielectric constant of the insulating layer can be established, and the current dielectric constant of the insulating layer can be obtained by online detection of the cable temperature, thereby reflecting the current damage of the insulation.

In this paper, the ambient temperature θ ₀ and the skin temperature θ _e are obtained by the fiber grating temperature monitoring system; the current I flowing in the conductor, the voltage to ground (phase voltage) U ₀ , the voltage frequency f, the angular frequency ω of the voltage, and the circumference ratio π are given as Known; metal shielding loss factor λ ₁ , armored/reinforced tape loss factor λ ₂ , equivalent insulating layer thermal resistance T ₁ , equivalent inner lining thermal resistance T ₂ , equivalent outer sheath thermal resistance T ₃ , equivalent External environmental thermal resistance T ₄ , conductor thermal capacity Q _c , insulating layer thermal capacity Q _i , inner lining thermal capacity Q _s , armor thermal capacity Q _cp , outer sheath thermal capacity Q _t , cable conductor AC resistance R, The insulation loss factor tgδ is calculated by the current IEC60287 standard.

Claims (3)

1. online insulation characterisitic determination methods of XLPE power cable; It is characterized in that: this determination methods is through setting up the hot road model of power cable; Try to achieve insulation course temperature and dielectric loss; And the relation of insulation thermal resistance, thereby set up the mathematical relation of temperature parameter and insulation course specific inductive capacity, through judge the damaged condition of current power cable insulation when the specific inductive capacity of front insulation layer.

2. the online insulation characterisitic determination methods of XLPE power cable according to claim 1 is characterized in that comprising the steps:

The first step is obtained the skin temperature at power cable point place and the environment temperature of this region;

Second step according to the electric current and the environment temperature that flow through in the known current conductor, calculated current conductor thread core temperature,

θ _c＝θ ₀+[T ₁+(1+λ ₁)*T ₂+(1+λ ₁+λ ₃)*(T ₃+T ₄)]*W _c+(0.5*T ₁+T ₂+T ₃+T ₄)*W _d

In the formula:

θ ₀The expression environment temperature,

θ _cExpression conductor thread core temperature,

λ ₁Expression metallic shield loss factor,

λ ₂Expression armouring/reinforcing band loss factor,

T ₃Represent equivalent outer jacket thermal resistance,

W _cRepresentation unit length of conductor power attenuation,

T ₂Represent equivalent inner liner thermal resistance,

W _dThe dielectric loss of representation unit length;

T ₁Represent equivalent insulation course thermal resistance,

T ₄Represent equivalent external environment condition thermal resistance;

In the 3rd step, obtain conductor thread core and insulation course temperature difference θ according to the hot road of power cable Model Calculation _Cm,

${\mathrm{\&theta;}}_{\mathrm{cm}}=(W_c+\frac{1}{2}*W_d)*T_1$

In the formula:

W _c＝I ²*R

$W_d=\mathrm{\&omega;}*c*U_0^2*\mathrm{tg\&delta;}$

ω＝2*π*f

Wherein:

W _cRepresentation unit length of conductor power attenuation,

T ₁Represent equivalent insulation course thermal resistance,

W _dExpression insulation loss, every meter of unit watt (W/m),

I representes the electric current that flows through in the conductor,

R representes the AC resistance of cable conductor,

ω representes the angular frequency of voltage,

C representation unit length cables electric capacity,

π representes circular constant,

F representes electric voltage frequency,

U ₀Be voltage-to-ground (phase voltage), unit volt (V),

Tg δ is the insulation loss factor,

The 4th step, the situation of change of the DIELECTRIC CONSTANTS through calculating this point, computing formula is:

$\mathrm{\&epsiv;}=\frac{18*({\mathrm{\&theta;}}_{\mathrm{cm}}-I^2*R*T_1)}{T_1*\mathrm{\&pi;}*f*U_0^2*\mathrm{tg\&delta;}}*\ln \left(\frac{D_i}{d_c}\right)*{10}^9$

In the formula:

θ _CmExpression conductor thread core and insulation course temperature difference,

I representes the electric current that flows through in the conductor,

R representes the AC resistance of cable conductor,

T ₁Represent equivalent insulation course thermal resistance,

π representes circular constant,

F representes electric voltage frequency,

U ₀Be voltage-to-ground (phase voltage), unit volt (V),

Tg δ is the insulation loss factor,

D _iExpression insulation course diameter,

d _cThe expression conductor diameter;

The 5th step, DIELECTRIC CONSTANTS and specific inductive capacity reference table that the 4th step was calculated compare, and draw judged result:

5.1 when the DIELECTRIC CONSTANTS that calculates be reduced to the specific inductive capacity reference table numeral 50% the time, must overhaul power cable;

5.2 when the DIELECTRIC CONSTANTS that calculates greater than the numeral of specific inductive capacity reference table 50% the time, show that state of insulation is normal.

3. the online insulation characterisitic determination methods of XLPE power cable according to claim 2 is characterized in that: the skin temperature at the power cable point place in the first step adopts the point measurement of optical fiber grating temperature monitoring system to obtain with the environment temperature of this region.

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