1. BRAZIL
ANDERSON RICARDO JUSTO DE ARAÚJO (speaker) RODRIGO CLEBER DA SILVA SÉRGIO KUROKAWA JUNE 2015
Improving the Performance of the Lumped Parameters transmission Line Model by Using Analog Low-Pass Filters

2. Overview Purposes Introduction Lumped parameters model
Distributed parameters model
Spurious oscillations
Analog low-pass filter
Conclusions
Acknowledgments
IPST 2015-Croacia

3. Purposes
The lumped parameters model (LPM) presents in its simulations intrinsic numeric spurious oscillations that do not represent the real value of the transient;
This work proposes an efficient method to improve the performance of the LPM used to simulate electromagnetic transients in electric power systems;
To mitigate these oscillations, an analog low-pass filter will be designed and inserted in the LPM;
To verify the proposed mitigating procedure, a single and three-phase transmission lines will be used to study the performance of proposed model;
IPST 2015-Croacia

4. Introduction
The currents and voltages along the line are described by differential equations whose solutions directly in time domain are not easily found;
the Lumped Parameters Model-LPM is a transmission line model used as an efficient model to represent single-phase and multiphase lines;
Advantages: It can be used for analyzing transients resulting from sudden changes in the network configuration, like as faults and opening/closing of circuit breakers;
It is directly developed in time domain and is compatible with the EMTP and ATP. It considers non-lineal loads, losses due the Corona Effect and faults caused by electric arcs.
IPST 2015-Croacia

5. Lumped Transmission Line
The transmission line can be represented by a n π-circuits cascade.
R and L are the series resistance and inductance of each segment.
G and C are the transversal conductance and capicitance of each segment.
d is the length line.
IPST 2015-Croacia

6. Heun´s numerical method
The longitundinal currents and the transversal voltages are depicted by state equations as shown in following.
Heun´s numerical method
IPST 2015-Croacia

7. Distributed Parameters Model
In the distributed parameters model all the electric parameters of line are distributed along the length line.
The current and voltage are evaluated from the frequency domain, considering the hyperbolic equations of the line (this model is also know as Universal Line Model-ULM).
Once obtained the solutions in frequency domain, the Inverse Laplace Transform is applied by numerical methods. So the response in time domain is obtained.
CBQEE/2015

8. Inverse Laplace Transform
Representation of the transmission line in frequency domain:
Hyperbolic Equations
Inverse Laplace Transform
This model presents the exact response for the current and voltage at receiving end of the line. So it will be used to compare the responses from the LPM.
CBQEE/2015

9. Results
A 100 km single-phase transmission line is represented by 100 π-circuits cascade.
The voltage at the receiving end B will be evaluated with the LPM and the ULM.
IPST 2015-Croacia

10. Spurious oscillations
These oscillations occur due the representation of a segment of line, whose parameters are distributed along the lenght line, by lumped elements of circuit.
They are independent of the numerical method used to solve the state equations .
Considering the first oscillation, its peak is 30% higher than exact response. This can result in improper performance on protection system or overestimation design of isolators for the transmission line.
IPST 2015-Croacia

11. Analog low-pass filter
To mitigate these spurious oscillations, it will be proposed a low-pass filter inserted directly in the LPM as shown.
Then the cut-off frequency fc of filter is equal to 47.3 kHz.
After to specific the low-pass filter, it was inserted in the LPM. It was observed that good results are obtained when filters are inserted at the two ends of the line represented by a π-circuit cascade.
IPST 2015-Croacia

12. The low-pass filter was inserted in the LPM at the two ends of the line represented by a cascade of π-circuits as it is shown.
The LPM, with two low-pass filters was used to simulate the energization of the single-phase transmission line shown above. It is possible to observe that lumped parameters line model with two analog filters mitigated the high frequency oscillations and reduced the magnitude peaks, making then similar to the peaks observed in ULM.
IPST 2015-Croacia

13. The analog filter was adequately projected and that proposed model is more efficient than LPM. The proposed model will be used to study electromagnetic transients in three-phase transmission line during the switching procedure.
IPST 2015-Croacia

14. The 4 and 5 are ground wires EHSW-3/8”.
To validate the proposed transmission line model with the analog low-pass filter inserted, it will be used a 440 kV three-phase transmission line whose transmission tower is presented as following.
Phases 1, 2 and 3 is constituted by 4 Grosbeak sub conductors (radius=1.021 cm).
The 4 and 5 are ground wires EHSW-3/8”.
The soil resistivity is 1000 Ω.m
the phase conductors are not transposed. It was considered a 100 km length.
IPST 2015-Croacia

15. a three-phase transmission line with a three-phase synchronous generator at sending end and balanced three-phase load Zload at the receiving end.
Zload =2000Ω
The modal decomposition theory was used for representing the three-phase transmission line. This way, the three-phase line can be decoupled in its three uncoupled single-phase transmission lines.
The voltages and currents are evaluated in modal domain for each phase.
Once obtained the modal currents and voltages, they are converted to the three-phase currents and voltages in phase domain.
IPST 2015-Croacia

16. LPM
Tensao VB(t)
ULM
LPM with Filters
IPST 2015-Croacia

17. a 440 kV/60 Hz synchronous generator connected at the sending end and a three-phase load at the receiving end. The line was energized with a synchronous three-phase generator at t=0 and, after ms, a 2 p.u. DC voltage source was applied at the sending end of the phase 1 during 0.3 ms. This voltage step was used to generate a disturb during the operation of the line in steady state.
IPST 2015-Croacia

18. ULM
LPM
One can observe that the spurious oscillations have been mitigating when low-pass filters are inserted in LPM and this response is similar to ULM.
The disadvantage consists on that inserting low-pass filter in the LPM, it causes a small shift in the responses in time domain that should be considered in the analysis, but all the responses converge in steady state
LPM with Filters
IPST 2015-Croacia

19. Conclusions .
This work has presented the improvement in the LPM including analog low-pass filters at the sending and receiving ends of the single-phase line represented by LPM.
Using the proposed model, it was possible to mitigate the spurious oscillations, reducing the magnitude of the peaks and then the response from LPM similar to ULM. The proposed filtering process is done simultaneously with the evolution of the simulations.
The proposed line model results in an efficient and friendly tool to represent transmission lines during simulations of the electromagnetic transients.
it can be easily inserted in electromagnetic transient programs like as ATP and EMTP and run the simulations in time domain.
IPST 2015-Croacia

20. Thank you !
Contacts:
IPST 2015-Croacia

21. Acknowledgments
Processo:
2014/
IPST 2015-Croacia