Available online at www.sciencedirect.com
ScienceDirect Procedia - Social and Behavioral Sciences 191 (2015) 179 – 184
WCES 2014
Advantages of Using MatLab Simulink in Laboratory Lessons on Operating Conditions of Overhead Power Lines Alexandru Baloi a *, Adrian Pana a, Florin Molnar-Matei a a
Politehnica University Timisoara,Piata Victoriei, No.2,Timisoara, 300006, Romania
Abstract The electrical power transmission is realised in most of the cases by overhead power lines long of hundred of kilometres and operating at different high voltage levels. The load of these overhead power lines is widely varying depending both on the evolution of consumers (the consumers load curve) and on the operating conditions of the power system elements. For experimental analysis of the operating conditions of transmission overhead power lines, the equivalent diagram П, T or Γ, generally symmetrical, are used. The paper presents the particular operating conditions of the overhead power lines: no load and short circuit, which are important in practice, because to their associated phenomena. A 400 kV overhead power line is modelled using MatLab Simulink and the above-mentioned operating conditions are analyzed. The presented model is used in teaching activity during the power grids laboratory lessons for power engineering students of our university. The paper includes the conclusions related to the studies and the detailed results. © byby Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2014The TheAuthors. Authors.Published Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of the Organizing Committee of WCES 2014. Selection and peer-review under responsibility of the Organizing Committee of WCES 2014 Keywords: Electrical engineering education, MatLab Simulink, transmission overhead power lines, particular operating conditions;
1. Introduction For long-distance electricity transmission, high voltages and very high voltages overhead power lines are used. These lines present a range of particular functional features, which are different than normal short lines used in electricity supply. The power flowing on an overhead power line, during the operation, can vary within relatively wide range. Corresponding to this variation, the values of voltages and currents vary. In order to appreciate the variation of voltage and current along the line in a certain situation, is very useful to know what is happen in some
* Alexandru Baloi. Tel.: +40-256-403-428 E-mail address:
[email protected]
1877-0428 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and peer-review under responsibility of the Organizing Committee of WCES 2014 doi:10.1016/j.sbspro.2015.04.367
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critical situations, characterized by limit values of voltage, current, or even transferred power and length. For these extreme conditions, quantitative conclusions regarding the variation of voltage and current can be found. So, to a certain regime depending how close is to one of those extreme regimes, qualitative assessments of changes in voltage and current can be done. The most common particular regimes are: no load and short-circuit. In the field of electrical engineering education, in addition to classical methods of teaching and testing the students’ knowledge (Smaill et al., 2012), engineering laboratories have become more and more complex, including simulation tools (Molnar-Matei et al., 2013). There are many simulation environments which can be used both for teaching several phenomena and also for research. In modern education methods, on line educational tools have an important role. In (Rodríguez et al., 2012) is presented an on-line mathematical tool for electrical circuits assessment and the results of motivating the students to use it. A student feedback is presented and the conclusion is that they agree to use such kind of mathematical tool. Nowadays, one of the most used simulation environments is MATLAB/Simulink. Technical education literature presents many publications about methods of MatLab Simulink modeling. A modeling technique for practical switched-mode power supplies design course is described in (Liao et al., 2012). In order to validate the correctness of the proposed method, four prototype circuits were studied and the conclusion is that the modeling technique can be successfully applied for switched-mode power supplies design. The feedback from students was also positive. MatLab GUI like mathematical tool to facilitate the study of interference and optical diffraction phenomena is used in (Francés et al., 2012). Another application of MatLab like a mathematical tool for teaching the autocorrelation function and noise concepts is presented in (Jovanovic Dolecek, 2012). In the field of electrical engineering, the most appropriate tool of Matlab Simulink is the SimPowerSystems library. In (Choi & Saeedifard, 2012) is presented a new educational power electronics laboratory that was developed primarily to reinforce experimentally the fundamental concepts presented in a power electronics course. In this paper, the particular operating conditions of overhead power lines are analysed using a Matlab Simulink model. Elements for electrical source, three phase distributed parameter line and measurements are used from SimPowerSystems Library. The results of the study and the conclusions are presented in detail in the paper. 2. Particular Operating Conditions of Overhead Power Lines: No Load, Short-Circuit, Natural Load Transmission overhead power lines are characterized by the fact that in the analysis of operating conditions should be considered a uniform distribution of electrical parameters (resistance and inductive reactance longitudinal conductance and transverse capacitive Susceptance) along the line. Because the line is usually the same throughout its construction, electrical parameters can be considered constant, resulting a homogenous line with the parameters Ru, Xu, Gu, Bu uniformly distributed. But, in steady state operating conditions, transmission overhead power lines are loaded balanced, so, the following phenomena can be followed on a single phase. Three-phase symmetrical line lossless can be characterized by the same equations as the homogeneous single phase line:
U f1 I1
U f2 cos 2S Lr jI 2 Z c sin 2S Lr I 2 cos 2S Lr j
U f2 Zc
sin 2S Lr
Where: Uf1, I1 are voltage and current at the begin of the line; Uf2, I2 – voltage and current at the end of the line; Zc – wave impedance (characteristic impedance); Lr – relative length of the line. 2.1. No load operating condition
(1)
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For this operating condition I2 = 0 and Z2 = Ğ. Following, equations (1) corresponding to lossless line becomes:
U f1 x U f2 cos 2S Lr U f2 I 1 x j sin 2S Lr Zc
(2)
In Fig.1 a) is presented the voltage and current variation along the line corresponding to no load operating condition. Analyzing expressions (2) and Fig.1 a) results: • the voltage at the beginning of the line and at every point of it is in phase with the voltage at the end of the line and the voltage at any point; • voltage and current vary sinusoidal along the line, and the current lead the voltage with a phase shift of π/2 electrical radians; • at the end of the line voltage is greater than at the beginning of the line, a phenomenon known as the Ferrantti effect (increase of voltage that occurs along the line at no load condition due to the capacitive character of the current which passes through the inductive reactance of the line); • the current varies sinusoidal along the line and is zero at the end of the line; • active power flowing on the line is zero, as in any section of line the current lead the voltage with a phase shift of π/2 (the real line absorbs from the source the active power necessary to cover losses). 2.2. Short-circuit operating condition For this operating condition Uf2 = 0 and Z2 = 0, following equations (1) corresponding to lossless line becomes:
U f1 jI 2 Z c sin 2S Lr I 1 I 2 cos 2S Lr
(3)
a) b) Fig. 1. Voltage and current variation along the line for the extreme operating conditions: a) no load, b) short-circuit
In Fig.1 b) is presented the voltage and current variation along the line for short-circuit operating condition. The analysis of relations (3) and Fig.1 b) show the following results: • current at the beginning of the line and current at any point of the line is in phase with the current at the end of the line; • current and voltage varies sinusoidal along the line and to the end of line (at the short-circuit point) the current is maximum;
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• in any section of the line the current is inductive, the current lag the voltage with a phase shift of π/2 electrical radians; • active power flowing on the line is zero. 3. Case Study In order to analyze the phenomena presented above, a 400 kV lossless overhead power line having 500 km length was modeled. The characteristic impedance for this line is ZC=320.87 Ω, and equivalent corresponding electric parameters per unit has the following values: Ru = 0,0345 Ω/km; Xu = 0,3446 Ω/km; Bu = 3,347•10-6 S/km; Gu = 0; Cu = 10,66•10-9 F/km. Considering the nominal voltage at the beginning of the line (Section 1) and applying the expressions (2) and (3) for the entire length of the line, the corresponding values for phase to neutral voltage and for the current corresponding to the end of the line (Section 2) are obtained. Also active and reactive powers can be determinate in the two sections of the line. The obtained values are presented in Table I. A MatLab Simulink model is used. The overhead transmission line is modeled using three phase PI section line element which is defined in SimPowerSystems Library. The line parameters presented above are used and the electrical source is modelled using the voltage level and the short-circuit power level. In Fig 2 and 3 are presented the MatLab Simulink models corresponding to no load respectively short-circuit operating conditions. Table 1. Application results Line
Electrical
Section
Amounts
Begin
End
Operating Conditions No Load
Short-Circuit
V [kV]
230
230
I [kA]
0.415
1.08
P [MW]
0
0
Q [MVAr]
287.52
745.2
V [kV]
266.66
0
I [kA]
0
1.443
P [MW]
0
0
Q [MVAr]
0
0
At the begging of the overhead power line, in case of no load operating conditions, the current has a capacitive character due to the natural capacities of the line and it produce to a negative voltage drop which will lead to an increase of the voltage at the end of the line, phenomena known as Ferrantti effect. For the study case presented in the paper, in can be remarked a voltage increase of about 15%, from 230 kV to 266.66 kV. In practice this voltage increase can become dangerous for the insulation and in order to avoid it, shunt inductive reactive compensation is done. In the case of short-circuit operating condition; the current has an inductive character.
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Fig.2 . Simulation results for no load operating condition.
Fig 3. Simulation results for short-circuit operating condition.
The character of the reactive power can be easy observed from the MatLab simulation diagram: the reactive power is positive for the inductive case, and negative for the capacitive case. This is a major advantage against the physical model, being very intuitive for the students. In the case when is need to know the values of the electrical amounts (voltage and current) in any section of the line, a simulation using two PI section lines can be done. 4. Conclusions Simulation software become more and more important in electrical engineering education due to some advantages against the hands-on models, but the later remains also very useful due to the similitude with the real industry installation. The paper presents the particular operating conditions of overhead power lines. The line is modelled using MatLab Simulink. A PI section line element is used here and the values of the electrical amounts at the beginning and at the end of the line are presented. The advantage against the classical physic model is that here it can be modelled the lossless line. The capacitive character of the reactive power at the beginning of the line in the case of
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no load operating condition can be remarked thanks to the three phase measurement block from SimPowerSystems Library, which displays a negative value. The voltage increase in this operating condition can become dangerous for the insulation line, and in practice shunt inductive reactive compensation is done in order to avoid it. A simulation using many PI section line can be done if the user desire to measure the voltage and current in any section of the line. In this case, when measurement blocks on the diagram become numerous, MatLab Simulink give the results centralized in a list which is accessible using powergui button, and there is the possibility to export it in other useful files format like xls spreadsheets. References Choi, S., & Saeedifard, M. (2012), An Educational Laboratory for Digital Control and Rapid Prototyping of Power Electronic Circuits, IEEE Transactions on Education, 55 (2), 263-270. doi: 10.1109/TE.2011.2169066 Francés, J., Pérez-Molina, M., Bleda, S., Fernández, E., Neipp, C., & Beléndez, A. (2012), Educational Software for Interference & Optical Diffraction Analysis in Fresnel and Fraunhofer Regions Based on MATLAB GUIs and the FDTD Method, IEEE Transactions on Education, 55 (1), 118-125. doi: 10.1109/TE.2011.2150750 Jovanovic Dolecek, G. (2012), MATLAB-Based Program for Teaching Autocorrelation Function and Noise Concepts, IEEE Transactions on Education, 55 (3), 349-356. doi: 10.1109/TE.2011.2176736 Liao, W.H., Wang, S.C., & Liu, Y.H. (2012), Generalized Simulation Model for a Switched-Mode Power Supply Design Course Using MATLAB/SIMULINK, IEEE Transactions on Education, 55 (1), 36-47. doi: 10.1109/TE.2011.2115243 Molnar-Matei, F., Iovan, M., & Maris, S., (2013), Mathematical Function of a Signal Generator for Voltage Dips Analysis, 15th International Conference on Computer Modelling and Simulation (UKSim). 10-12 April, Cambridge, 569 – 574. Rodríguez, S.B., Fuertes, M.C., Piera, A.F., Garcia, I.P., & Arcega Solsona, F.J. (2012), Lessons Learned in the Use of WIRIS Quizzes to Upgrade Moodle to Solve Electrical Circuits, IEEE Transactions on Education, 55 (3), 412-417. doi: 10.1109/TE.2011.2181381 Smaill, C.R., Rowe, G.B., Godfrey, E., & Paton, R.O. (2012), An Investigation Into the Understanding and Skills of First-Year Electrical Engineering Students, IEEE Transactions on Education, 55 (1), 29-35. doi: 10.1109/TE.2011.2114663
