CN112461386B - Method for calculating discharge resistance temperature in high-voltage direct-current submarine cable test - Google Patents
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Abstract
The invention discloses a method for calculating discharge resistance temperature in a high-voltage direct-current submarine cable test, which comprises the following steps: determining a current parameter of the discharge resistor by combining the submarine cable capacity, the voltage grade and the discharge resistor; according to the structure of the discharge resistor, calculating the time integral of the through-flow thermal effect power of the discharge resistor to obtain a heat measurement formula of the discharge resistor with unit length; calculating the heat dissipation power of the discharge resistor in unit length by using convection and radiation principles; calculating to obtain the temperature increment of the discharge resistor at each delta t time; and obtaining the peak time of the temperature and the corresponding temperature value, wherein the maximum temperature value is the maximum temperature occurring in the test. The method can effectively obtain the temperature increment and the temperature value of the discharge resistor in each delta t time in the discharge resistance test, obtain the maximum temperature value appearing in the discharge resistance test, solve the problem that the discharge resistance temperature in the high-voltage direct-current submarine cable test cannot be calculated, and reduce the safety risk in the discharge test operation.
Description
Technical Field
The invention belongs to the technical field of electric power, and particularly relates to a method for calculating discharge resistance temperature in a high-voltage direct-current submarine cable test.
Background
The completion test of the high-voltage direct-current submarine cable line requires that direct-current voltage withstand test equipment is used for charging, pressurizing and bearing for a certain time to test the insulation performance of the cable, and the direct-current submarine cable line has long transmission distance and large capacity, so that discharge resistance is easily overheated in the discharge process to damage discharge equipment.
However, there is no method for effectively monitoring the temperature of the discharge resistor, which brings a great safety risk to the discharge test operation.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the method for calculating the discharge resistance temperature in the high-voltage direct-current submarine cable test is provided, the problem of calculation of the discharge resistance temperature can be solved, and a basis is provided for test discharge.
The technical scheme is as follows: in order to achieve the purpose, the invention provides a method for calculating the discharge resistance temperature in a high-voltage direct-current submarine cable test, which comprises the following steps:
s1: determining a current parameter of the discharge resistor by combining the submarine cable capacity, the voltage grade and the discharge resistor;
s2: according to the structure of the discharge resistor, calculating the time integral of the through-flow thermal effect power of the discharge resistor to obtain a heat measurement formula of the discharge resistor in unit length, and obtaining the heat production of each discharge resistor in unit length according to the heat measurement formula;
s3: calculating the heat dissipation power of the discharge resistor in unit length by using convection and radiation principles;
s4: by utilizing the law of conservation of energy, taking the discharge starting time as 0 time, taking a certain time delta t to perform iterative calculation on time, calculating heat production, heat dissipation and heat absorption in a resistance unit of unit length of each delta t time, and calculating to obtain the temperature increment of the discharge resistance at each delta t time;
s5: and recording the time of the first negative temperature increment of the discharge resistor with unit length continuously bearing the discharge current after the total discharge resistance value is changed for the first time, and obtaining the peak time of the temperature and the corresponding temperature value according to the time, wherein the maximum temperature value is the maximum temperature appearing in the test.
Here, the times at which the negative temperature increase occurs for the first time are Δ t (X1 + 1), Δ t (X2 + 1), …, and Δ t (XM + 1), respectively, and the times at which the temperature peaks occur are (Δ t (X1), TX 1), (Δ t (X2), and TX 2) … … (Δ t (XM), and TXM), respectively, and Tmax = MAX (TX 1, TX2, … …, and TXM), respectively, which is the maximum temperature at which the test occurs. The time period during which the maximum temperature occurs is the time during which the highest temperature occurs in the discharge resistance discharge test.
Further, in the step S1, a current parameter of the discharge resistor is determined through a current function;
the current function is I = U/R EXP [ -1/(R C) ];
the discharge current of each discharge resistor is as follows: i = U/(R × P) EXP [ -1/(R × C) ];
wherein U is the initial voltage of the high-voltage direct-current cable; r is the total resistance of the discharge resistor; p is the parallel number of discharge resistors.
Further, the formula of the heat generated by measuring the unit length discharge resistance in step S2 is as follows:
∫R2*U0^2/(R^2*P^2)*EXP[-1/(RC)]dt＝R2*C*U0^2/(R*P^2)*{1-EXP[-2*t/(R*C)]}
wherein U is the initial voltage of the high-voltage direct-current cable; r is the total resistance of the discharge resistor; p is the parallel number of discharge resistors.
Further, the method for calculating the heat dissipation power of the unit length discharge resistor in the step S3 includes: respectively acquiring convection heat dissipation power, radiation heat dissipation power and heat absorption energy;
convection heat dissipation power: w1= h a (T-T0);
radiation heat dissipation power: w2=4 ∈ σ ^ (T ^4-T0^ 4);
wherein T is the current temperature;
according to joule's law, the endothermic energy is;
W3＝θ*m*(T-T0)；
therefore, the heat dissipation power of the discharge resistor per unit length is the convective heat dissipation power + the radiant heat dissipation power, i.e., W1+ W2.
Further, the specific calculation process of the temperature increment in step S4 is as follows:
1 st Δ t: the method comprises the steps that a discharge resistor generates heat in delta T1/0.5 × convection heat dissipation power temperature conduction function Δ T1+0.5 × radiation heat dissipation power leads to a function value Δ T1+ specific heat capacity × unit length discharge resistor mass at an initial temperature T0, and a discharge resistor temperature increment delta Δ T1 is obtained through calculation, wherein the discharge resistor temperature T1= the initial temperature T0+ Δ T1;
2 nd Δ t: the discharge resistor generates heat in a delta T2, the discharge resistor 1 generates heat in a delta T2 at the temperature of T1, the convective heat dissipation power temperature derivative function is 0.5, the radiant heat dissipation power is 0, the temperature derivative value is delta T2+ the specific heat capacity is the unit length discharge resistor mass at the temperature of T1, the temperature increment delta T2 of the discharge resistor is obtained through calculation, and the temperature T2 of the discharge resistor is = T0+ delta T1+ delta T2;
……
nth Δ t: the method comprises the steps that a discharging resistor generates heat in delta tN, a radiating power temperature transfer function delta tN +0.5 convectional radiating power temperature transfer function delta tN +0.5 radiative radiating power generates radiating power in delta tN under the temperature of a discharging resistor T (N-1), discharging resistor temperature increment delta TN is obtained through calculation, and the discharging resistor temperature T (N + 1) = T0+ delta T1+ … … + delta T (N-1) + delta TN is obtained through calculation;
n +1 th Δ t: and calculating the temperature increment of the discharge resistor delta T2 and the temperature T (N + 1) = T0+ delta T1+ … … + delta T (N + 1) of the discharge resistor under the temperature delta T (N + 1) heat generation-discharge resistor TN/0.5 x heat dissipation power temperature conduction function delta T (N + 1) +0.5 x radiation heat dissipation power at the temperature lead value of TN (delta T + 1) + specific heat capacity x unit length discharge resistor mass, and calculating to obtain the temperature increment of the discharge resistor delta T2 and the temperature T (N + 1) = T0+ delta T1+ … … + delta T (N + 1).
According to the method, a discharge current function related to time is obtained by using the capacity, the voltage grade and the discharge resistance parameters of the submarine cable, and a unit length discharge resistance measurement heat function is obtained by calculating the time integral of the discharge resistance through-flow thermal effect power by using the structure of the discharge resistance; the method comprises the steps of obtaining a heat dissipation function related to time and temperature by using a convection and radiation heat dissipation power equation, taking a certain time delta t as a starting point to carry out temperature iterative calculation, calculating heat generation, heat dissipation and heat absorption capacity in a resistance unit of unit length of each delta t time unit, obtaining a temperature increment and a temperature value of a discharge resistor in each delta t time unit, and obtaining a maximum temperature value appearing in a discharge resistor test through comparison.
Has the beneficial effects that: compared with the prior art, the method and the device have the advantages that through application of technologies such as a time function, a discharge resistance heat measurement function, a heat dissipation function, temperature iterative calculation and the like, the temperature increment and the temperature value of the discharge resistance in each delta t time in a discharge resistance test can be effectively obtained, the maximum temperature value appearing in the discharge resistance test is obtained, the problem that the discharge resistance temperature cannot be calculated in a high-voltage direct-current submarine cable test is solved, the temperature monitoring of the discharge resistance is realized, and the safety risk existing in the discharge test operation is greatly reduced.
Drawings
FIG. 1 is a diagram of a typical structure of a discharge resistor;
FIG. 2 is a circuit schematic of a discharge process;
fig. 3 is an explanatory diagram of heat generation and heat dissipation of the discharge resistor per unit length.
Detailed Description
The invention is further elucidated with reference to the drawings and the embodiments.
The invention provides a method for calculating discharge resistance temperature in a high-voltage direct-current submarine cable test, which comprises the following steps in combination with figure 2:
s1: determining a current parameter of the discharge resistor through a current function by combining the submarine cable capacity, the voltage grade and the discharge resistor;
calculating a current function as I = U/R EXP < -1/(R < - > C >) according to a zero input response principle of a section of circuit;
the discharge current of each discharge resistor is as follows: i = U/(R × P) EXP [ -1/(R × C) ].
Wherein U is the initial voltage of the high-voltage direct-current cable; r is the total resistance of the discharge resistor; p is the parallel number of discharge resistors.
S2: according to the structure of the discharge resistor, calculating the time integral of the through-flow thermal effect power of the discharge resistor to obtain a heat measurement formula of the discharge resistor in unit length, and obtaining the heat production of each discharge resistor in unit length according to the heat measurement formula;
the formula for measuring heat generation of the discharge resistor with unit length is as follows:
∫R2*U0^2/(R^2*P^2)*EXP[-1/(RC)]dt＝R2*C*U0^2/(R*P^2)*{1-EXP[-2*t/(R*C)]}。
s3: calculating the heat dissipation power of the discharge resistor in unit length by using convection and radiation principles;
respectively acquiring convection heat dissipation power, radiation heat dissipation power and heat absorption energy,
convection heat dissipation power: w1= h a (T-T0);
radiation heat dissipation power: w2=4 ∈ σ ^ (T ^4-T0^ 4);
wherein T is the current temperature;
according to joule's law, the endothermic energy is;
W3＝θ*m*(T-T0)；
therefore, the heat dissipation power of the discharge resistor per unit length is the convective heat dissipation power + the radiant heat dissipation power, i.e., W1+ W2.
S4: by utilizing the law of conservation of energy, taking the initial discharge time as 0 time, taking a certain time delta t to perform iterative calculation on time, calculating heat production, heat dissipation and heat absorption in a resistance unit of unit length of each delta t time, and calculating to obtain the temperature increment of the discharge resistance in each delta t time by referring to FIG. 3;
the specific calculation process of the temperature increment is as follows:
1 st Δ t: the method comprises the steps that a discharge resistor generates heat in delta T1/0.5 × convection heat dissipation power temperature conduction function Δ T1+0.5 × radiation heat dissipation power leads to a function value Δ T1+ specific heat capacity × unit length discharge resistor mass at an initial temperature T0, and a discharge resistor temperature increment delta Δ T1 is obtained through calculation, wherein the discharge resistor temperature T1= the initial temperature T0+ Δ T1;
2 nd Δ t: the discharge resistor generates heat in a delta T2, the discharge resistor 1 generates heat in a delta T2 at the temperature of T1, the convective heat dissipation power temperature derivative function is 0.5, the radiant heat dissipation power is 0, the temperature derivative value is delta T2+ the specific heat capacity is the unit length discharge resistor mass at the temperature of T1, the temperature increment delta T2 of the discharge resistor is obtained through calculation, and the temperature T2 of the discharge resistor is = T0+ delta T1+ delta T2;
……
nth Δ t: the method comprises the steps that a discharging resistor generates heat in delta tN, a radiating power temperature transfer function delta tN +0.5 convectional radiating power temperature transfer function delta tN +0.5 radiative radiating power generates radiating power in delta tN under the temperature of a discharging resistor T (N-1), discharging resistor temperature increment delta TN is obtained through calculation, and the discharging resistor temperature T (N + 1) = T0+ delta T1+ … … + delta T (N-1) + delta TN is obtained through calculation;
n +1 th Δ t: the heat generation in the discharge resistor delta T (N + 1) -the heat dissipation in the delta T (N + 1)/the convection heat dissipation power temperature conduction function delta T (N + 1) + 0.5-the radiation heat dissipation power at the temperature of the discharge resistor delta T (N + 1) -the specific heat capacity and the discharge resistor quality in unit length, the discharge resistance temperature increment Δ T2 and the discharge resistance temperature T (N + 1) = T0+ Δ T1+ … … + Δ TN + Δ T (N + 1) are calculated.
S5: recording the time when the negative temperature increase first occurs in the discharge resistor per unit length which is continuously subjected to the discharge current after the total discharge resistance value is changed for the first time, as Δ t (X1 + 1), Δ t (X2 + 1), …, and Δ t (XM + 1), the peak time of the temperature occurs, the temperature as (Δ t (X1), TX 1), (Δ t (X2), TX 2) … … (Δ t (XM), TXM), tmax = MAX (TX 1, TX2, … …, TXM), and the maximum temperature of the test. The time period during which the maximum temperature occurs is the time during which the highest temperature occurs in the discharge resistance discharge test.
Based on the above method, the method of the present invention was applied to the test in this example.
Regarding the discharge resistance parameters:
as shown in fig. 1, the space structure of the discharge resistor is 4-node series connection, and the total resistance R0 is 10M Ω; each resistor R1 is 2.5 MOmega, the number P of the parallel resistors of each resistor is 10, and each resistor R2 is 25 MOmega; each discharge resistor is of a ceramic structure and a tubular structure, the outer diameter r2 is 55mm, and the inner diameter r1 is 45mm; the density rho is 2700kg/m3; the specific heat capacity theta is 850J/(kg DEG C); the discharge resistance mass m per unit length was calculated to be 1.696kg and the surface area A was calculated to be 0.1413m2.
Regarding sea cable parameters:
the test voltage U0 is 580kV; the capacitance C is 20uF;
regarding the heat dissipation parameters:
the convection heat dissipation coefficient h is 3.42W/(m ^ 2*K);
the radiation heat radiation emissivity is epsilon 0.9, and is dimensionless;
Stefan-Boltzmann constant σ is 5.67 x 10 (8), and m2 x K4;
the method of the invention is utilized to obtain the following formula:
ΔT1＝R2*C*U0^2/(R*P^2)*{1-EXP[-2*t/(R*C)]}/{0.5*h*A*Δt1+2*ε*σ*T0^3*Δt1+θ*m}；T1＝T0+ΔT1,t1＝Δt1；
ΔT2＝R2*C*U0^2/(R*P^2)*EXP[-2/(RC)*t1]*{1-EXP[-2*Δt2/(RC)]}-h*T1*Δtn-4*ε*A*σ*[T1^4-T0^4]/{0.5*h*A*Δt2+2*ε*σ*T1^3*Δt2+θ*m}，T2＝T1+ΔT2，t2＝t1+Δt2；
ΔTn＝R2*C*U0^2/(R*P^2)*EXP[-2/(R*C)*t(n-1)]*{1-EXP[-2*Δtn/(R*C)]}-h*T(n-1)*Δtn-4*ε*A*σ*[T(n-1)^4-T0^4]/{0.5*h*A*Δtn+2*ε*σ*T0^3*Δtn+θ*m}，Tn＝T(n-1)+ΔTn；tn＝t(n-1)+Δtn。
let Δ t1= Δ t1= … = Δ tn = Δ t, then:
ΔTn＝{R2*C*U0^2/(R*P^2)*EXP[-2/(R*C)*(n-1)*Δt]*{1-EXP[-2*Δt/(R*C)]}-h*T(n-1)*(n-1)*Δt-4*ε*A*σ*[T(n-1)^4-T0^4]}/{0.5*h*A*Δt+2*ε*σ*T0^3*Δt+θ*m}，Tn＝T(n-1)+ΔTn。
in this embodiment, the environmental temperature is measured at 20 ℃, Δ T =1s, the discharge resistance is not changed by the discharge, and the temperature is substituted into T0, Δ T, R2, C, U, R, P, h, a, ∈, σ, θ, and m, and the following data is obtained by calculation:
it can be seen that the initial difference temperature increment of the 178 th iteration calculation is negative, which indicates that the temperature appearing in the 177 th iteration is the highest temperature appearing in the iteration, the discharge resistance value of the test discharge is not changed, and the highest temperature of the discharge resistance of the current discharge test is 55.99 ℃.
Claims (4)
1. A method for calculating discharge resistance temperature in a high-voltage direct-current submarine cable test is characterized by comprising the following steps:
s1: determining a current parameter of the discharge resistor by combining the submarine cable capacity, the voltage grade and the discharge resistor;
s2: according to the structure of the discharge resistor, calculating the time integral of the through-flow thermal effect power of the discharge resistor to obtain a heat measurement formula of the discharge resistor in unit length, and obtaining the heat production of each discharge resistor in unit length according to the heat measurement formula;
s3: calculating the heat dissipation power of the discharge resistor in unit length by using convection and radiation principles;
s4: by utilizing the law of conservation of energy, taking the initial discharge time as 0 time, taking a certain time delta t to perform iterative calculation on the time, calculating the heat production, heat dissipation and heat absorption in the unit of the resistance in unit length of each delta t time, and calculating to obtain the temperature increment of the discharge resistance in each delta t time;
s5: recording the time of the first negative temperature increment of the discharge resistor with unit length continuously bearing the discharge current after the total discharge resistance value is changed for the first time, and obtaining the peak time of the temperature and the corresponding temperature value according to the time, wherein the maximum temperature value is the maximum temperature appearing in the test;
the specific calculation process of the temperature increment in the step S4 is as follows:
1 st Δ t: the method comprises the steps that a discharge resistor generates heat in delta T1/0.5 × convection heat dissipation power temperature conduction function Δ T1+0.5 × radiation heat dissipation power leads to a function value Δ T1+ specific heat capacity × unit length discharge resistor mass at an initial temperature T0, and a discharge resistor temperature increment delta Δ T1 is obtained through calculation, wherein the discharge resistor temperature T1= the initial temperature T0+ Δ T1;
2 nd Δ t: the method comprises the steps that a discharging resistor generates heat in a delta T2, heat dissipation in the delta T2/0.5 x convection heat dissipation power temperature-dependent function delta T2+0.5 x radiation heat dissipation power generates heat in the delta T2, the temperature-dependent function value delta T2+ the specific heat capacity x unit length discharging resistor quality is obtained through calculation, and discharging resistor temperature increment delta T2 is obtained, wherein the discharging resistor temperature T2= T0+ delta T1+ delta T2;
……
nth Δ t: the method comprises the steps that a discharge resistor generates heat in delta tN, a convection heat dissipation power temperature conduction function delta tN +0.5 x convection heat dissipation power temperature conduction function is set at delta tN, radiation heat dissipation power is set at a TN temperature conduction value delta tN + specific heat capacity x unit length discharge resistor mass, discharge resistor temperature delta TN is obtained through calculation, and discharge resistor temperature T (N + 1) = T0+ delta T1+ … … + delta T (N-1) + delta TN is set at a temperature T (N-1);
n +1 th Δ t: and calculating the temperature increment of the discharge resistor delta T (N + 1) and the temperature T (N + 1) = T0+ T1+ … … + TN + T (N + 1) of the discharge resistor under the temperature delta T (N + 1) of heat generation-discharge resistor TN/0.5 + T radiation power temperature conduction function value delta T (N + 1) + heat transfer capacity + T0.5 + radiation power at the temperature TN and the discharge resistor quality per unit length.
2. The method for calculating the discharge resistance temperature in the high-voltage direct current submarine cable test according to claim 1, wherein the method comprises the following steps: in the step S1, a current parameter of the discharge resistor is determined through a current function;
the current function is I = U/R EXP [ -1/(R ×) and;
the discharge current of each discharge resistor is as follows: i = U/(R × P) EXP [ -1/(R × C) ];
wherein U is the initial voltage of the high-voltage direct-current cable; r is the total resistance of the discharge resistor; p is the parallel number of discharge resistors.
3. The method for calculating the discharge resistance temperature in the high-voltage direct current submarine cable test according to claim 1, wherein the method comprises the following steps: the formula for measuring heat generation of the unit length discharge resistor in the step S2 is as follows:
∫R2*U0^2/(R^2*P^2)*EXP[-1/(RC)]dt＝R2*C*U0^2/(R*P^2)*{1-EXP[-2*t/(R*C)]}。
4. the method for calculating the discharge resistance temperature in the high-voltage direct current submarine cable test according to claim 1, wherein the method comprises the following steps: the method for calculating the heat dissipation power of the unit length discharge resistor in the step S3 comprises the following steps: respectively acquiring convection heat dissipation power, radiation heat dissipation power and heat absorption energy,
convection heat dissipation power: w1= h a (T-T0);
radiation heat dissipation power: w2=4 ∈ σ ^ (T ^4-T0^ 4);
wherein T is the current temperature;
according to joule's law, the endothermic energy is:
W3＝θ*m*(T-T0)；
therefore, the heat dissipation power of the discharge resistor per unit length is the convective heat dissipation power + the radiant heat dissipation power, i.e., W1+ W2.
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