A Calculation Method for Dynamic Capacity Increase of Dual-Circuit Trenched Cables Based on Typical System Components

Abstract

This invention relates to a dynamic capacity expansion calculation method for dual-circuit trench cables based on typical system components. The method first calculates the transient temperature rise curve of the dual-circuit cable under a given step load using the system component method. Second, it plots the overload current-operating time curve of the dual-circuit trench cable. Finally, it can quickly determine the maximum safe operating time under a given overload current, and the maximum allowable current under a given operating time. Compared with existing technologies, this invention has advantages such as higher calculation accuracy and shorter calculation time.

Description

Technical Field

[0001] This invention relates to the field of dynamic capacity expansion technology for cables, and in particular to a method for calculating dynamic capacity expansion of dual-circuit trench cables based on typical system components. Background Technology

[0002] In recent years, with the rapid development of my country's economy, the demand for industrial and residential electricity has increased significantly, making the bottleneck problem of power transmission capacity increasingly severe. Dynamic capacity expansion technology for transmission lines is one of the important measures to improve transmission capacity. Compared with other line capacity expansion technologies, such as improving conductor materials and adjusting transmission structure, dynamic capacity expansion technology has the advantages of low investment and short construction period, making it a major research and development direction for improving line transmission capacity in various countries. Currently, my country's standard for cable current carrying capacity is calculated based on the most stringent external environment (such as ambient temperature, wind speed, and solar radiation power). Therefore, under normal conditions, the allowable steady-state current carrying capacity of cable lines is always less than the actual operating current carrying capacity of the line, meaning that the line's current carrying capacity is not fully utilized. The principle of dynamic capacity expansion technology is to calculate the current carrying capacity of the line in real time based on the measured actual external environmental conditions, so as to fully utilize the power transmission capacity of the transmission line.

[0003] When the core temperature of a cable reaches its maximum permissible operating temperature, the load current in the cable is called the cable's maximum current carrying capacity. For example, for cross-linked polyethylene (XLPE), a commonly used insulating material, the maximum permissible operating temperature is 90°C. Therefore, the maximum current carrying capacity is the load current corresponding to a core temperature of 90°C. It is evident that the main factor limiting cable transmission capacity is the temperature of the cable core. Thus, to implement dynamic capacity expansion technology, the current temperature of the cable core must first be calculated based on external environmental conditions and the cable's current actual current carrying capacity. Then, the dynamic capacity expansion capacity can be calculated. The sum of the current actual current carrying capacity and the dynamic capacity expansion capacity is the maximum permissible current carrying capacity of the cable under the current operating conditions.

[0004] Dynamic capacity expansion calculations for cables mainly include two aspects: 1) calculating the safe operating time given an overload current when the electrical load suddenly increases; 2) calculating the allowable overload current when other lines need to bear a certain overload during a line outage for maintenance, given the outage and maintenance time. Existing calculation methods generally suffer from low accuracy and long calculation times. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a dynamic capacity expansion calculation method for dual-circuit trench cables based on typical system components.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] According to one aspect of the present invention, a method for dynamic capacity expansion calculation of dual-circuit trench cables based on typical system components is provided. The method first uses the system component method to calculate the transient temperature rise curve of the dual-circuit cable under a given step load, then plots the overload current-operating time curve of the dual-circuit trench cable, and finally, the maximum safe operating time can be quickly found under a given overload current, and the maximum allowable current can be quickly found under a given operating time.

[0008] As a preferred technical solution, the method specifically includes the following steps:

[0009] Step S1: Construct a physical model of a dual-loop trench cable and use the finite element method to calculate the transient temperature rise curves of the cable core under different step loads.

[0010] Step S2: Treat the transient temperature rise of the cable with applied step load current as the step output response of a certain undetermined system, and construct the transfer function between the input and output of the system by combining typical components of the system.

[0011] Step S3: Based on the transient temperature rise curves under different step loads obtained by the finite element method in step S1, determine the undetermined parameters in the transfer function, and then obtain the transfer function of the system.

[0012] Step S4: Calculate the steady-state temperature rise of the cable core under different initial loads using the finite element method, and use it as the initial value of the transient temperature rise curve. Input a unit step signal into the system, and use the transfer function determined in step S3 to calculate the output curve of the system, which is used as the obtained transient temperature rise curve of the cable core.

[0013] Step S5: Based on the transient temperature rise curves of the cable core under different initial loads and step loads, calculate the time required for the cable core temperature to reach the maximum allowable temperature, and plot the step load-time curves under different initial loads.

[0014] Step S6: When a step increase in capacity (i.e., overload current) is given, the maximum allowable safe operating time is found based on the step load-time curve; when an operating time is given, the maximum allowable increase in capacity is found based on the step load-time curve.

[0015] As a preferred technical solution, step S1 establishes a physical model of the dual-loop trench cable and uses the finite element method to simulate and calculate the transient temperature rise curves of the two loop cores under different step loads, wherein the step loads I1 and I2 of the two loops are given independently.

[0016] As a preferred technical solution, the physical model of the dual-circuit trench cable includes heat conduction, radiative heat transfer, and convective heat transfer of air within the trench.

[0017] As a preferred technical solution, step S2 specifically includes:

[0018] Take one phase cable of one loop of a double-loop trench cable as the system under consideration, and assume it to be a single-input single-output system. The input is a unit step signal and the output is the transient temperature rise curve of the cable core. The relationship between the input and the output is represented by a transfer function. The transfer function adopts a combination of typical elements. The transfer function of the inertial element and the integral element in parallel is taken as the transfer function of the system.

[0019] Let the transfer functions of the inertial element and the integrator element of system 1 corresponding to loop 1 be as follows:

[0020]

[0021]

[0022] In the formula, G 11 (s) and G 12 (s) are the transfer functions of the inertial element and the integrator element of system 1, respectively; K1 is the amplification factor of the inertial element, T1 is the inertial time constant, and T... I1 The integral time constant;

[0023] After connecting the inertial element and the integrator in parallel, the transfer function of system 1 is:

[0024]

[0025] Similarly, the transfer function of system 2 is:

[0026]

[0027] In the formula, G1(s) and G2(s) are the transfer functions of system 1 and system 2, respectively, where K1, K2, T1, T2, and T are the transfer functions of system 1 and system 2, respectively. I1 T I2 These are parameters to be determined.

[0028] As a preferred technical solution, the phase cable is the one with the highest temperature in the finite element method simulation calculation results.

[0029] As a preferred technical solution, in step S3, the undetermined parameters of the transfer function are expressed as a function of the step load current. The specific form of the function is obtained by fitting the calculation results of the finite element method in step S1. The specific steps are as follows:

[0030] Step 3.1, within the set range, determine the parameter group (K1, T1, T) I1The process involves iterating through the parameters. After each set of parameters is selected, the unit step response curve of the transfer function G1(s) is compared with the transient temperature rise curve of the cable core of loop 1 obtained by finite element method simulation. The sum of the temperature rise errors between the two at all time points within the transient calculation time range is calculated, as shown in the following formula:

[0031]

[0032] In the formula, T G,i and T C,i The values ​​are the temperature rise of the cable core of loop 1 obtained by simulation calculation using the current method and the finite element method at the i-th time node, respectively, and N is the number of time nodes within the selected transient duration;

[0033] Step 3.2: Select the set (K1, T1, T) that minimizes ΔT. I1 If the optimal parameter set is substituted into the transfer function G1(s) of system 1, the optimal G1(s) is obtained. At this time, the unit step response of system 1 is uniquely determined, and the response curve is closest to the result of the finite element method simulation.

[0034] Step 3.3: Set the optimal parameter group (K1, T1, T) under different working conditions (I1, I2). I1 The function is fitted to I1 and I2, i.e.:

[0035] K1=f1(I1,I2),T1=f2(I1,I2),T I1 =f3(I1,I2)

[0036] Step 3.4: The transfer function G2(s) of loop 2 corresponding to system 2 is also determined using the steps shown in steps 3.1 to 3.3.

[0037] As a preferred technical solution, in step S4, the temperature rise of the cable core under constant load is calculated by the finite element method, and this is used as the initial value of the transient temperature rise curve of the cable core under the corresponding initial load; unit step signals are input to system 1 and system 2 respectively, and the output curves obtained by G1(s) and G2(s) transformation are the transient temperature rise curves of the cable core of loop 1 and loop 2 calculated by this method.

[0038] As a preferred technical solution, the maximum allowable temperature of the cable core in step S5 is 90°C for XLPE insulated cables.

[0039] As a preferred technical solution, in step S6, the step load-time curve drawn in step S4 is used as the basis. If an overload current is given, the corresponding maximum safe operating time is found through the curve; if an allowable safe operating time is given, the corresponding maximum allowable overload current is found through the curve.

[0040] Compared with existing technologies, this invention uses the system link method to calculate the transient temperature rise curve of a dual-circuit cable under a given step load, and on this basis, plots the overload current-operating time curve of the dual-circuit trench cable. Under a given overload current, the maximum safe operating time can be quickly found, and under a given operating time, the maximum allowable current can be quickly found. It has the advantages of high calculation accuracy and short calculation time. Attached Figure Description

[0041] Figure 1 This is a flowchart of the method of the present invention;

[0042] Figure 2 This is a schematic diagram of the physical model of an embodiment of the method of the present invention, which is a dual-circuit trench cable;

[0043] Figure 3 This is a schematic diagram of the cable body in an embodiment of the method of the present invention, wherein 1 is a conductor, 2 is an insulation layer, 3 is a metal sheath, and 4 is an outer sheath;

[0044] Figure 4 This is a schematic diagram of a typical system component combination of the method of the present invention;

[0045] Figure 5 This is the overload current-safe operating time curve of the method of the present invention under an initial load of 600A;

[0046] Figure 6 This is the overload current-safe operating time curve of the method of the present invention under the condition of an initial load of 800A. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0048] like Figure 1 As shown, this invention proposes a rapid calculation method for dynamic capacity expansion of dual-circuit trench cables. Given an overload current, the maximum safe operating time can be calculated; given an operating time, the maximum allowable overload can be calculated.

[0049] Figure 2 This is a schematic diagram of a dual-loop trench cable, with the two loops named Loop 1 and Loop 2. The dimensions of the trench cable are shown in the diagram. The cable body structure is as follows. Figure 3As shown, the cable type is 8.7 / 15kV YJV 1×400. A physical model of the trench cable was constructed, and independent step loads were applied to the two circuits respectively. The transient temperature changes of the cable cores of the two circuits over time were calculated using the finite element software COMSOL. Different load applications correspond to different operating conditions, as shown in Table 1. In the table, I1 and I2 are the step load currents of circuit 1 and circuit 2, respectively.

[0050] Table 1 COMSOL Step Load Condition Data

[0051] <![CDATA[I1 / A]]> 500 500 500 500 800 800 800 800 <![CDATA[I2 / A]]> 500 700 900 1100 500 700 900 1100

[0052] The transient temperature rise of a dual-loop trench cable under different step loads is calculated using the system element method. For example... Figure 4 As shown, the system consists of an inertial element and an integrator connected in parallel. The input is a unit step signal representing the step load current, and the output represents the transient temperature rise curve of the cable core. In this embodiment, regardless of the value of the step load, the input is always a unit step signal, and the influence of different step load values ​​is included in the undetermined parameters of the transfer function.

[0053] Let loop 1 and loop 2 correspond to system 1 and system 2 respectively, then the transfer function of system 1 is:

[0054]

[0055] The transfer function of system 2 is:

[0056]

[0057] In the formula, G1(s) and G2(s) are the transfer functions of system 1 and system 2, respectively, where K1, K2, T1, T2, and T are the transfer functions of system 1 and system 2, respectively. I1 T I2 These are parameters to be determined.

[0058] Taking System 1 as an example, this illustrates the method for determining the undetermined parameters in the transfer function. Taking a specific operating condition from Table 1, a set of undetermined parameter values ​​(K1, T1, T) is selected by iterating through a certain range. I1 Within the considered operating conditions, K1 is set to [5, 30], T1 to [5000, 7000], and T... I1 Take [0.5×10] 5 1.5×10 5 During the traversal process, after each set of parameters is selected, the unit step response curve of the transfer function G1(s) is compared with the transient temperature rise curve of the cable core of loop 1 calculated by COMSOL. The sum of the temperature rise errors between the two at different time points is calculated, as shown in the following formula:

[0059]

[0060] In the formula, T G,i and T C,i These represent the difference between the temperature rise of the cable core of loop 1 calculated by the system link method and COMSOL at the i-th time node, respectively, and N is the total number of time nodes within the selected transient duration of 3000 min. In this embodiment, a time node is selected every 1 min.

[0061] Traverse and retrieve the parameter set (K1, T1, T) I1 After that, select the set (K1,T1,T) that minimizes ΔT. I1 () as the optimal parameter set.

[0062] The optimal parameter sets (K1, T1, T) under different working conditions (I1, I2) shown in Table 1 are... I1 The function was fitted to I1 and I2, and the fitting results are as follows:

[0063] K1=0.0044I1+0.052I2-17.94, R 2 =0.9996

[0064] T1=3.89I1+0.17I2-0.003I1I2+4372, R 2 =0.9999

[0065] R 2 =0.9997

[0066] The transfer function G2(s) of loop 2 corresponding to system 2 is determined using the same method as that of system 1, (K2,T2,T) I2 The fitting results are as follows:

[0067] K2=0.0049I1+0.0015I2-14.77, R 2 =0.9997

[0068] T2=-3.72I1-5.75I2+0.005I1I2+8757, R 2 =0.9999

[0069] R 2 =0.9997

[0070] Assuming that the initial loads of loop 1 and loop 2 are the same, namely 600A and 800A respectively, the highest temperatures of the cable core of loop 1 under steady state are calculated using COMSOL to be 313.05K and 328.16K respectively.

[0071] Keeping the load current of loop 2 constant at the initial load, a given overload current is applied to loop 1. The overload is expressed in per-unit value, i.e., overload current = overload multiple × rated current, where the rated current refers to the steady-state current corresponding to the highest allowable temperature of the cable core reaching 90°C under steady-state operation conditions of the dual loops. In this embodiment, the rated current value of the dual-loop trench cable is calculated to be 1235A using COMSOL. The five overloads applied to loop 1 in this embodiment are shown in Table 2:

[0072] Table 2 Different Overload Conditions of Circuit 1

[0073] Overload current / A 1482 1729 1976 2223 2470

[0074] The highest temperature of the cable core of loop 1 calculated by COMSOL at 600A and 800A was used as the initial value for transient calculation. The total transient calculation time was taken as 3000min. The transient temperature rise curve of the cable core of loop 1 was calculated by using the system link method when the initial load was 600A and 800A respectively.

[0075] In this embodiment, the insulation material is XLPE, and the maximum operating temperature is 90℃. Transient temperature rise curves were calculated using both COMSOL and the system link method to determine the time corresponding to the temperature rise reaching 90℃. The results are shown in Table 3.

[0076] Table 3. Time required for the cable core temperature to reach 90℃ under different operating conditions using the method of the present invention and COMSOL calculation.

[0077]

[0078] As shown in Table 3, the maximum relative error between the time required for the cable core temperature to reach 90℃ calculated using the method of the present invention and the result calculated by COMSOL is within 3%, indicating that the calculation results of the rapid capacity increase capability of dual-circuit trench cables using the method of the present invention are relatively accurate.

[0079] Plot Table 3 as a line graph, such as... Figure 5 and Figure 6 As shown in the figure, the maximum safe operating time under a given overload current, or the maximum allowable overload current under a given operating time, can be quickly found from the graph.

[0080] This invention provides a rapid calculation method for dynamic capacity expansion of dual-circuit trench cables. It can calculate the maximum safe operating time based on a given overload current, or the maximum allowable overload based on a given operating time, combining both calculation accuracy and speed.

[0081] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for dynamic capacity expansion calculation of a double circuit duct cable based on typical links of a system, characterized in that, This method first uses the system link method to calculate the transient temperature rise curve of a double-circuit cable under a given step load, then plots the overload current-operating time curve of the double-circuit trench cable, and finally, the maximum safe operating time can be quickly found under a given overload current, and the maximum allowable current can be quickly found under a given operating time. The method specifically includes the following steps: Step S1: Construct a physical model of a dual-loop trench cable and use the finite element method to calculate the transient temperature rise curves of the cable core under different step loads. Step S2: Treat the transient temperature rise of the cable with applied step load current as the step output response of a certain undetermined system, and construct the transfer function between the input and output of the system by combining typical components of the system. Step S3: Based on the transient temperature rise curves under different step loads obtained by the finite element method in step S1, determine the undetermined parameters in the transfer function, and then obtain the transfer function of the system. Step S4: Calculate the steady-state temperature rise of the cable core under different initial loads using the finite element method, and use it as the initial value of the transient temperature rise curve. Input a unit step signal into the system, and use the transfer function determined in step S3 to calculate the output curve of the system, which is used as the obtained transient temperature rise curve of the cable core. Step S5: Based on the transient temperature rise curves of the cable core under different initial loads and step loads, calculate the time required for the cable core temperature to reach the maximum allowable temperature, and plot the step load-time curves under different initial loads. Step S6: When the step increase capacity is given, the maximum allowable safe operating time is found according to the step load-time curve; when the operating time is given, the maximum allowable increase current is found according to the step load-time curve. Step S2 specifically involves: Take one phase cable of one loop of a double-loop trench cable as the system under consideration, and assume it to be a single-input single-output system. The input is a unit step signal and the output is the transient temperature rise curve of the cable core. The relationship between the input and the output is represented by a transfer function. The transfer function adopts a combination of typical elements. The transfer function of the inertial element and the integral element in parallel is taken as the transfer function of the system. Let the transfer functions of the inertial element and the integrator element of system 1 corresponding to loop 1 be as follows: In the formula, G 11 ( s )and G 12 ( s ) are the transfer functions of the inertial element and the integrator element of system 1, respectively; K 1 represents the amplification factor of the inertial element. T 1 represents the inertial time constant. T I1 The integral time constant; After connecting the inertial element and the integrator in parallel, the transfer function of system 1 is: Similarly, the transfer function of system 2 is: In the formula, G 1( s )and G 2( s ) are the transfer functions of system 1 and system 2, respectively. K 1. K 2. T 1. T 2. T I1 , T I2 These are parameters to be determined.

2. The method for dynamic capacity expansion calculation of dual-circuit trench cables based on typical system components according to claim 1, characterized in that, In step S1, a physical model of the dual-loop trench cable is established, and the transient temperature rise curves of the two loop cores under different step loads are simulated and calculated using the finite element method. The step loads I1 and I2 of the two loops are given independently.

3. The method for dynamic capacity expansion calculation of dual-circuit trench cables based on typical system components according to claim 2, characterized in that, The physical model of the dual-circuit trench cable includes heat conduction, radiative heat transfer, and convective heat transfer of air within the trench.

4. The method for dynamic capacity expansion calculation of dual-circuit trench cables based on typical system components according to claim 1, characterized in that, The aforementioned phase cable is the one with the highest temperature in the finite element method simulation results.

5. The method for dynamic capacity expansion calculation of dual-circuit trench cables based on typical system components according to claim 1, characterized in that, In step S3, the undetermined parameters of the transfer function are expressed as a function of the step load current. The specific form of the function is obtained by fitting the calculation results of the finite element method in step S1. The specific steps are as follows: Step 3.1, within the set range, the parameter group to be determined ( K 1, T 1, T I1 The function iterates through the data, retrieving each set of parameters. After each set is selected, the function is passed the result. G 1( s The unit step response curve of the circuit is compared with the transient temperature rise curve of the loop 1 cable core obtained by finite element method simulation. The sum of the temperature rise errors between the two at all time points within the transient calculation time range is calculated as shown in the following formula: In the formula, T G,i and T C,i The first i The temperature rise of the cable core of loop 1 obtained by simulation calculation using this method and the finite element method at each time point. N This represents the number of time points within the selected transient duration. Step 3.2: Take a value that makes Δ T The smallest group ( K 1, T 1, T I1 If we substitute these optimal parameter sets into the transfer function of system 1, we can determine the optimal parameter set. G 1( s In this process, the optimal solution is obtained. G 1( s At this point, the unit step response of system 1 is uniquely determined, and the response curve is closest to the result of the finite element method simulation. Step 3.3: Different working conditions ( I 1, I 2) Optimal parameter set ( K 1, T 1, T I1 Fitted as I 1. I A function of 2, namely: ， ， Step 3.4: Transfer function of system 2 corresponding to loop 2 G 2( s The same steps as shown in steps 3.1 to 3.3 are used to determine this.

6. The method for dynamic capacity expansion calculation of dual-circuit trench cables based on typical system components according to claim 1, characterized in that, In step S4, the temperature rise of the cable core under constant load is calculated using the finite element method, and this is used as the initial value of the transient temperature rise curve of the cable core under the corresponding initial load; a unit step signal is input to system 1 and system 2 respectively, and then... G 1( s )and G 2( s The output curve obtained by the transformation is the transient temperature rise curve of the cable core of loop 1 and loop 2 calculated by this method.

7. The method for dynamic capacity expansion calculation of dual-circuit trench cables based on typical system components according to claim 1, characterized in that, The maximum permissible temperature of the cable core in step S5 is 90 °C for XLPE insulated cables.

8. The method for dynamic capacity expansion calculation of dual-circuit trench cables based on typical system components according to claim 1, characterized in that, In step S6, based on the step load-time curve drawn in step S4, if an overload current is given, the corresponding maximum safe operating time is found through the curve; if an allowable safe operating time is given, the corresponding maximum allowable overload current is found through the curve.

Images