Abstract

 

The high voltage impulses are usually generated under experimental conditions with the purpose of imitating actual internal and external voltages which are referred to as switching and lightning voltages respectively. Related laboratory configurations are expensive and not with sufficient accuracy. Therefore, this project describes the development of switching and lightning impulse simulator using MATLAB software. The objective is to develop a simple model to simulate the actual switching and lightning impulse through MATLAB Graphical User Interface (MATLAB GUI) software and comparing the results with the required IEC standards. In addition, background information, theoretical equations and possible circuits that can be applied to generate the high voltage impulses are discussed. The equation and circuit analysis of impulse voltage generators are used to achieve a rewarding approximation of 1.2/50 and 250/2500 impulse voltages.

Keywords: MATLAB, Impulse Voltage Generator, Lightning Impulses, Switching Impulses.

 

Table of Contents

 

Chapter 1. 1

1.1.      Introduction. 1

1.2.      Theoretical Relevance. 2

Chapter 2. 2

2.1.      Impulse Voltages Concept 2

2.1.1        Lightning Impulse Voltage. 2

2.1.2        Switching Impulse Voltage. 1

2.2.      Impulse Waveform.. 1

2.3.      Impulse Generator Circuit 2

2.4.      Impulse Equations. 3

Chapter 3. 5

3.1.      Impulse Circuit Parameters Determination. 5

3.2.      Simulation Outcomes. 6

3.3.      GUI Development 7

3.4.      Future work. 7

3.5.      Project Timeline. 8

3.6.      Conclusion. 8

References. 9

Appendix 1. 9

 

 

 

 

 

 

 

Chapter 1        

1.1.    Introduction

The growth in the electrical energy demand has led to higher capacity and larger dimensions of power systems equipment. Such a trend entails more reliable power systems equipment including transmission lines, transformers, circuit breakers, and insulators towards a superiror quality and effectiveness achievement. The high voltages that are generated by abnormalities such as faults and lightning initiate transient voltage across power systems components which in turn significantly affect the dielectric strength of their insulation. Therefore, seeking an appropriate material for insulation, selective tests are conducted on the material towards assessing its robustness against transient voltages.

Most of the disturbances in the electric transmission systems are caused by the transient overvoltages due to lightning and switching impulses. The impulses occur when the amplitude of the overvoltage surpasses the normal alternating current voltages. Switching and lightning surge tests are consequently essential to be conducted on any equipment employed in the high voltage systems. The impulses developed on this project are therefore only used to test high voltage apparatus.

In a typical double exponential wave, the wave steadily rises to a peak value before falling back to its initial value. Therefore, several parameters have to be specified to completely describe an impulse or surge wave. These parameters include the peak value voltage, rise time, and fall time at 50% of the peak value voltage [1]. In a circuit, the impulse or surge waves can be generated by a set of R-C circuits or R-L-C circuits in more advanced forms. The values of R and C in an impulse generator circuit can be manipulated to set the rise time and fall time. To control output impulse waveform, the resistance, R, is varied while the capacitance of the generator and the load are held constant according to the object under test [2]. Size of the capacitor would have to be small to allow the fast charging and discharging with single capacitor is the circuit. However, generted voltages would not provide sufficient amplitude to produce an impulse waveform. Thus, this project employs two capacitors, and  in the impulse generator circuit [3]. These two capacitors will be charged in parallel to achieve the maximum impulse voltage, and then discharged in series to use the shortest discharge time possible. This approach was previously introduced by a German Engineer called Erwin Otto Marx in early 1924 [4].

The objective of this project is to design a lightning impulse circuit and to use this circuit to generate impulse or surge voltages in MATLAB/Simulink employing its Graphical User Interface (GUI). Generated results are then will be compared to IEC and Australian standards.

1.2.    Theoretical Relevance

The Australian Standards (AS), as well as the International Electro-technical Commission (IEC), have provided required standards to realize a quality testing of high voltage equipment [5]. For a high voltage equipment to be completely approved for installment, it has to withstand switching and lightning impulse waveforms. Once test object is approved, it is able to withstand any form of voltage surges stemming from natural factors such as lightning. While most researchers focus on the abnormality of the impulse waves, the study on the generation and control of these waves has not received extensive coverage.

 

 

Chapter 2

2.1.    Impulse Voltages Concept

When over-voltages appear in distribution and transmission systems, two major factors are involved. These include the lightning impulses due to lightning and the switching impulses due to the operational switching in the network.

2.1.1        Lightning Impulse Voltage

The major cause of impulse voltages is the lightning impulse [6]. For power systems that are equipped with lightning protection mechanisms, the waves through the system are generally transformed by the lightning protection equipment. Therefore, lightning impulses waves will have different forms and shapes. This alteration in the waveforms is mathematically expressed through the double exponential terms as follows [7]

 

The terms  and  are time constants while V₀ represents the charging/discharging voltage. Therefore, the lightning voltage can also be expressed in form of a double exponential waveform. It can be inferred that output wave rises to a peak value and then falling back to its initial value. To attain a satisfactory approximation of the impulse, peak value, rise time, and fall time are critical features. The impulse generally has a sharp rise to a peak value and then declines more smoothly to the original value. While the rise time is affected by ?, fall time is controlled by ?. Consequently, the former value is expected to be smaller than the later one. It is critical to determine these values in order to imitate the same waveform for different applications.

2.1.2        Switching Impulse Voltage

Another cause of the impulse voltages is the switching overvoltages which stems from the switching operations within the power system. The switching operations within the power systems include the distribution feeder switching, capacitor banks switching in the utility and the circuit breaker switching [8]. For instance, when de-energized capacitors are switched in a domestic utility to provide reactive power, the voltage will drop to zero temporarily as the voltage across a capacitor cannot vary instantaneously. The voltage then stabilizes back through a series of oscillations which may creat an overshoot voltage almost twice the amplitude of the sinusoidal waveform. The same effects occur whenever the capacitor bank is switched off. However, the time scale is larger compared with lightning ones.

2.2.    Impulse Waveform

IEC standards have set a guideline for the generation of the impulse waveforms [9]. According to this standards, any designed circuit towards impulse waveforms genration should produce waveforms equal to switching impulse as well as lightning impulse. IEC standards specify that the standard rise time is between  and  while the standard fall time is between  and  [10]. The target for this project is to develop an impulse with  and  rise time and  and  fall time which is well within IEC standards. IEC standard waveform of the impulse voltage is illustrated in Figure ?2?1. Full impulse waveform according to Australian Standard is illustrated in Figure ?2?2.

Figure ?2?1: Full impulse waveform according to IEC Standards [10]

The maximum voltage (peak) according to both Figure ?2?1 and Figure ?2?2 is stated as 100% while other important points such as D (B in Figure ?2?2) represent 90% of peak and C (A in Figure ?2?2) represents 30% of peak. The point  represents the origin of the impulse waveform. Both IEC and Australian Standards specify the rise time as a product of 1.67 to the time interval between 30% and 90% of peak. These standards also specify that there is a standard tolerance for the rise time and   for the fall time. Consequently, associeted specification can be expressed as follows,
Figure ?2?2: Full impulse waveform according to Australian Standards

For this project, to respect IEC standards, the rise time in the range of  to  and the fall time between  and  is acceptable for the  model. For the  model, the rise time ranges from  to  and the fall time ranges from  to .

2.3.    Impulse Generator Circuit

R2

The circuit presented in Figure ?2?3 is considered as impulse generator circuit in this study which includes two resistors  and  and two capacitors  and  where  reperesents the test material [11].

Figure ?2?3: Impulse Generator Circuit [12]

2.4.    Impulse Equations

Considering illustrated circuit in Figure ?2?3, the output voltage across capacitor  can be expressed as follows

 

Taking the Laplace transformation equation,

 

Using the circuit to obtain the currents through  and ;

 

 

Considering equation ,  and ,

 

Roots of equation can be calculated as follows;

 

 

Considering the output of the circuit given in Figure ?2?3;

 

Therefore, the impedance equivalent of the circuit can be obtained from out of circuit elements.

 

The impedance values can be represented as follows;

 

 

Substituting these two equations into equation ;

 

where

 

 

 

Performing anti-Laplace transform;

 

where  represent the roots of  such that;

 

Therefore, since  and  will be predetermined,  and are obtained as;

 

 

Therefore, to obtain  and a table of  and  is given as;

 

Table ?2?1: Time Constant Values for Waveforms

1.2/5	3.480	0.800
1.2/50	68.2	0.405
1.2/200	284.0	0.381
250/2500	2877	104.0

Chapter 3

 

3.1.    Impulse Circuit Parameters Determination

As C₁ and C₂ are generally predetermined, the impulse should be set through changing resistors.

 

 

 

Then, R₁ and R₂ can be determined considering the following equations which are simplified mathematical models with the purpose of parameters determination [13].

 

where T_f and T_r are constant values. The front, tail and virtual origin times are calculated as follows,

T_front= t₉₀-t_{60                                                                                                                                                                                              }

T_tail= t₅₀ – Virtual Origin

Virtual Origin=

where t₉₀ and t₆₀ refer to the time associated with 90 and 30% of peak value in the impulse during rise time and t₅₀ is the time related to 50% of peak value during fall interval.

3.2.    Simulation Outcomes

Outcomes are provided for two modes of 1.2/50 and 250/2500. For both cases we assume C₁= 0.5?f and V=1 (Equation 5). Other parameters are as follows

1.2/50: C₂= 12.5nf; R₁= 33 ?; R₂= 134?.

250/2500: C₂= 78.49nf; R₁= 1.245k ?; R₂= 5.912k ?.

Following figures illustrates output results associated with 1.2/50 and 250/2500 modes respectively.

Figure ?3?1: Generated Impulse for 1.2/50 Mode

Figure ?3?2: Generated Impulse for 250/2500 Mode

Related front and tail times are according to the following values;

1.2/50: T_front= 1.16?s; T_tail= 49.15?s.

250/2500: T_front= 239.81?s; T_tail= 2534?s.

As it was mentioned, capacitor values should respect a standard ratio to each other with the purpose of generating either of impulse waveforms. Therefore, it is not possible to test any test object with the designed impulse generator configuration considering its internal capacitance (C₁).

3.3.    GUI Development

A GUI window was programmed to make impulse generator simulator increasingly user-friendly (see Figure ?3?3). This simulator draws both lightning and switching curves according to the entries in the left hand side for illustrated circuit parameters.

After determining required values for impulse waveform generation applying equation , this simulator uses these input values to conduct calculations and sketch associated curve after pushing “RUN” button. Meanwhile, T_front and T_tail  are calculated and represented in the left down side of window as output values. Respecting IEC 60060-1 standard tolerance, allocated output windows will turn green. Otherwise, they are programmed to turn red implying that entry values are not acceptable towards generating a standard waveform.

3.4.    Future work

Further research will be conducted on the impulse generator considering more advanced Circuit of multistage generator which is also called as Marx generator.Also, improve (GUI) to be more educated.

****((The above sentence I added it to let you know the work you will do)).

The motivation is to address difficulties related to one-stage circuit including corona discharges in the configuration and connected leads, configuring extra-high DC voltage sources towards charging C₁, and required space of embedded components.

 

 

Figure ?3?3: Generated Impulse for 250/2500 Mode

3.5.    Project Timeline

Different stages are scheduled according to Table ?3?1.

Table ?3?1: Project Timeline

Time Frame	Task
Week 1-2	Initial Review
Week 3	Project Finalization
Week 4-6	Detailed Literature Review and Initial Design
Week 7-9	Software Design (Simulations) and Hardware Design (if possible)
Week 10-11	Detailed Project Report and Abstract
Week 12	End of Semester Report and Poster Demonstration
Week 13	Project Seminar Presentation
Next Semester	The course will be held with more advanced circuitry including inductance component in the configuration

3.6.    Conclusion

In this project, the concepts of impulse waveforms were discussed and associated mathematical concepts were applied to MATLAB software towards imitating switching and lightning impulses. Impulse waveforms related to 1.2/50 and 250/2500 waveform modes were generated. According to IEC standard, the typical rise time is between 1.2?s and 250?s while the standard fall time is between 50?s and 2500?s. According to the IEC standards, rise time is defined as the product of 1.67 to the interval between associated times of 30 and 90% of peak value. There is an acceptable tolerance equals to ±30% and ±20% for the rise and fall time respectively. Therefore, accomplished values in the previous section are all acceptable as they respect IEC standard.

 

References

[1]        L. Moura and I. Darwazeh, Introduction to linear circuit analysis and modelling: from DC to RF. Burlington, Mass;Oxford;: Newnes, 2005.

[2]        A. v. Meier, Electric power systems: a conceptual introduction. Hoboken, N.J: IEEE Press, 2006.

[3]        L. Patidar and H. Sawarkar, “Impulse Testing of Power Transformers For Effective Resistors Using Orcad Pspice,” International Journal Of Scientific Research And Education, vol. 2, 2014.

[4]        V. V. Tatur, “Modification of Marx generator with a doubling of output voltage,” International Journal of Circuit Theory and Applications, vol. 43, pp. 415-420, 2015.

[5]        E. F. Fuchs, M. A. S. Masoum, and I. Books24x, Power quality in power systems and electrical machines. Amsterdam;Boston;: Academic Press/Elsevier, 2008.

[6]        A. Pfeffer and S. Tenbohlen, “Evaluation of parameters of lightning impulse voltages from transformer tests using the new k-factor approach,” IEEE Transactions on Dielectrics and Electrical Insulation, vol. 17, pp. 947-952, 2010.

[7]        W. Jia and Z. Xiaoqing, “Double-Exponential Expression of Lightning Current Waveforms,” pp. 320-323.

[8]        S. A. Ali, “Capacitor banks switching transients in power systems,” Energy Science and Technology, vol. 2, pp. 62-73, 2011.

[9]        “BS 923-1:1990, IEC 60060-1:1989: Guide on high-voltage testing techniques. General,” ed: British Standards Institute, 1990.

[10]      B. Hesterman and D. Powell, “Introduction To Voltage Surge Immunity Testing,” in Proc. IEEE Power Electron. Soc. Denver Chapter Meeting, 2007.

[11]      E. Kuffel, J. Kuffel, and W. S. Zaengl, High voltage engineering: fundamentals vol. 2nd;2;. Oxford: Newnes, 2000.

[12]      V. K. Verma, “Practical Simulation and Modelling of Lightning Impulse Voltage Generator using Marx Circuit,” National Institute of Technology Rourkela, 2014.

[13]      M. S. Kamarudin, E. Sulaiman, M. Z. Ahmad, S. A. Zulkifli, and A. F. Othman, “Impulse Generator and Lightning characteristics simulation using Orcad Pspice software,” presented at the 2nd Regional Engineering Conference, Kuching, Sarawak, Malaysia, 2008.

Appendix 1

• MATLAB Code for Impulse Generation

clc

clear

 

%% 1.2/50

R1=33;

R2=134;

C1=5*10^-7;

C2=125*10^-10;

 

%% 250/2500

% R1=1245;

% R2=5912;

% C1=5*10^-7;

% C2=78.49*10^-9;

 

A=(C2.*R1).^-1;

B=(C1*R2)^-1;

 

 

t=0:10^-7:10^-2;

V=((R2*C1*A*B*1)/(B-A)).*(exp(-A.*t)-exp(-B.*t));

 

peak=0;

for i=1:size(t,2)

if V(i)<=.3*max(V) && peak==0

t30=t(i);

elseif V(i)<=.9*max(V) && peak==0

t90=t(i);

else

peak=1;

end

if V(i)>=.5*max(V) && peak==1

t50=t(i);

end

end

&nbsp;

Origin=t30-.5*(t90-t30);

&nbsp;

Front=1.67.*(t90-t30);

Tail=t50-Origin;

&nbsp;

plot(t,V)

grid on

&nbsp;