- freely available
Energies 2019, 12(1), 67; https://doi.org/10.3390/en12010067
2. ETN Modeling of Overhead Transmission Lines
2.1. Heat Transfer Analysis of Overhead Transmission Line Cross-Section
2.2. ETN of Overhead Transmission Lines
3. Transient Temperature Calculation Method for Overhead Transmission Line Based on the ETN
3.1. Determination of ETN Parameters
3.2. Transient Temperature Calculation Method with Nonlinear Iteration
- Step 1:
- Acquire conductor parameters, meteorological parameters, and current, and determine the initial values of Q, C, and R of the ETN by Equations (8)–(18). The initial temperature of each node is ambient temperature TE.
- Step 2:
- Calculate temperature of each node by Equation (7), and modify resistivity, radiant heat of nodes, and thermal convection resistance by Equations (11), (13) and (18), correspondingly. Thus, the temperature values of each node of the ETN can be solved.
- Step 3:
- Assess whether the temperature difference between two adjacent iterations satisfies the control precision (considered 0.01 °C in this paper). Otherwise, set the number of iterations l to l + 1, and continue the calculation until the temperature difference is less than that of the given precision.
- Step 4:
- Adjust the Joule heat of nodes of the ETN by current. Use the temperature value outputted in Step 3 as the initial value of the transient temperature rise response calculation for subsequent iterations.
- Step 5:
- Determine whether the calculation is completed. Otherwise, set time tn = tn−1 + ∆t for the calculation until the calculation time is equal to the prescribed time.
- Step 6:
- Obtain the calculation results of the transient temperature rise response, and the calculation is completed.
4. Experimental Verification of the Model and Calculation Method
4.1. Temperature Rise Test Platform of Overhead Transmission Lines
4.2. Verification of the Model and Calculation Method
4.3. Extrapolation and Validation
5. MPTP Based on the Transient Temperature of Overhead Transmission Lines
5.1. Transient Temperature Estimation of the Entire Overhead Transmission Lines
5.2. MPTP Strategy of Overhead Transmission Lines
- Step 1:
- Initialize talarm and Wline to 0. Determine whether the operating current IL is greater than the maximum load current ILmax. Proceed to Step 2 when the start-up criterion of protection IL > ILmax is satisfied.
- Step 2:
- Obtain the meteorological parameters around the transmission line and conductor parameters. Then, modify the ETN in real-time by Equations (22) and (23), and calculate the transient temperature rise response. Proceed to Step 3.
- Step 3:
- Assess whether the calculated Tline is greater than the limit temperature TL. Send a trip signal to the dispatching system and the breaker of the transmission line to remove the line when criterion Tline > TL is satisfied. End the MPTP algorithm. Proceed to Step 4 when the Tline does not exceed TL.
- Step 4:
- Determine whether the calculated Tline is greater than the emergency temperature TM. Otherwise, proceed to Step 5. Evaluate the talarm using Equation (26) when criterion Tline > TM is satisfied, and calculate the temperature–time integral Wline. Then, verify the emergency thermal setting value Wset using Equation (27), and compare the values of Wline and Wset. If the criterion Wline > Wset is satisfied, a trip signal to the dispatching system and the breaker cuts off the line, and the algorithm ends. If the criterion Wline > Wset is not satisfied, an emergency warning signal is sent to the dispatching system, and the algorithm returns to Step 2 to continue the calculation of transient temperature rise and thermal safety assessment for transmission line.
- Step 5:
- Assess whether the calculated Tline is greater than the alarm temperature TN. Send an alarm signal to the dispatching system and start the talarm when criterion Tline > TL is satisfied. Furthermore, return to Step 2. Proceed to Step 6 when criterion Tline > TN is unsatisfied.
- Step 6:
- Determine whether operating current IL is lower than return current KreILmax (Kre is the return coefficient, generally set to 0.9). End the protection algorithm when criterion IL ≤ KreILmax is satisfied. Otherwise, return to Step 2, and continue the calculation of the transient temperature rise response and thermal safety assessment of the transmission line.
6. Case Study for Protection of Overhead Transmission Lines
6.1. Test System
6.2. Results and Discussion
- Case I:
- Line L3 is in a normal operation, Line L1 trips at t = 120 s due to a fault, and Line L2 is overloaded.
- Case II:
- Line L3 is disconnected due to maintenance, Line L1 trips at t = 120 s due to a fault, and Line L2 is overloaded.
- Case III:
- Line L3 is disconnected due to maintenance, Line L1 trips at t = 120 s due to a fault, and Line L2 is overloaded, which is in accordance with Case II. However, the power flow is adjusted by power system security and stability controls. Thus, the current of Line L2 is reduced at t = 600 s.
- Conductor cross-section heat transfers under overloading conditions can be characterized in three types, namely, radial and circumferential heat conduction, convection, and radiation. The ETN can integrate the above-mentioned types and simultaneously reflect the temperature-dependent characteristics of resistivity, thermal convection resistance, and radiant heat flux. The comparison of the calculated results with the experimental results shows that the calculation precision of the ETN is better than the IEEE and CIGRE standard models. The calculated relative error does not exceed 7.59% under 95% confidence interval.
- The transient temperature estimation of transmission lines based on ETN can objectively characterize the dynamic safety state of the entire line. In comparison with the DTLR, the proposed method can better reflect the effects of non-uniform meteorological distribution along the line and the different temperature rise responses in different parts of the transmission line.
- The MPTP of the transmission line can provide more time than the TOP when eliminating overloads. The delay time of the MPTP does not reduce transmission line security, which is derived from the electro-thermal coupling analysis of the line. The MPTP calculation time can satisfy the engineering requirements, as confirmed by the case study.
Conflicts of Interest
|Name||Model Number||Main Specification|
|Steel frame||Self-made||0.8 × 0.8 × 2.0 m|
|Large current generator||SDDL-5000Q||Rated capacity: 30 kVA|
Output current: 0–5000 A
Accuracy: 0.1 %
|Controllable blower||HB-429||Wind speed: 0–10 m/s|
|Current transformer||LXZK-0.66||Ratio: 3200/5 A|
Rated Burden: 15 VA
Accuracy: 0.2 %
|Temperature sensor||PT1000||Range: −70 °C–+500 °C|
Accuracy: ±0.03 °C (class 1/10B)
|Ultrasonic anemometer||HY-WDS3||Range: 0–60 m/s, 0–359°|
Resolution: 0.01 m/s, 0.1°
|Radiation intensity measuring instrument||SPN1||Range: 0–2000 W/m2|
Resolution: 0.6 W/m2
|Multi-channel data acquisition device||Agilent 34970A & 34901A||Scan rate:250 Channels/s|
Resolution: 22 bits
|Conductor outside diameter D0 (mm)||26.82|
|Steel core diameter (mm)||7.5|
|Aluminum outer strand diameter (mm)||3.22|
|Sectional area (mm2)||425.24|
|Emissivity ε 1||0.9|
|Solar absorptivity δ 2||0.9|
|Steel specific heat capacity at 20 °C, cs (J/kg· °C)||481|
|Aluminum specific heat capacity at 20 °C, ca (J/kg· °C)||897|
|Steel mass per unit length, ms (kg/m)||0.267|
|Aluminum mass per unit length, ma (kg/m)||1.079|
|Mass per unit length of steel (kg/m)||1.349|
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|Current (A)||Wind Speed (m/s)|
|Current (A)||Air Temperature ( °C)||Wind Speed (m/s)|
|Regions||Air Temperature ( °C)||Wind Speed 1 (m/s)||Radiation Intensity (W/m2)|
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